On Shift Operators

1988 ◽  
Vol 31 (1) ◽  
pp. 85-94 ◽  
Author(s):  
J. R. Holub
Keyword(s):  
Banach Space ◽  
Separable Hilbert Space ◽  
Shift Operator ◽  
Continuous Functions ◽  
Usual Definition ◽  
Shift Operators ◽  
Spaces Of Continuous Functions ◽  
Backward Shift ◽  
The Common ◽  
Definition Of

AbstractA definition of an isometric shift operator on a Banach space is given which extends the usual definition of a shift operator on a separable Hilbert space. It is shown that there is no such shift on many of the common Banach spaces of continuous functions. The associated ideas of a semi-shift and a backward shift are also introduced and studied in the case of continuous function spaces.

scholarly journals BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY

2007 ◽  
Vol 49 (1) ◽  
pp. 145-154
Author(s):  
BRUCE A. BARNES
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Integral Operators ◽  
Continuous Functions ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Closed Range ◽  
Bounded Linear ◽  
Spaces Of Continuous Functions

Abstract.LetTbe a bounded linear operator on a Banach spaceW, assumeWandYare in normed duality, and assume thatThas adjointT†relative toY. In this paper, conditions are given that imply that for all λ≠0, λ−Tand λ −T†maintain important standard operator relationships. For example, under the conditions given, λ −Thas closed range if, and only if, λ −T†has closed range.These general results are shown to apply to certain classes of integral operators acting on spaces of continuous functions.

scholarly journals The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space

2013 ◽  
Vol 21 (3) ◽  
pp. 185-191
Author(s):  
Keiko Narita ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Banach Space ◽  
Integral Operator ◽  
Real Banach Space ◽  
Closed Interval ◽  
Continuous Functions ◽  
Real Numbers ◽  
Riemann Integral ◽  
Basic Properties ◽  
Bounded Functions ◽  
Definition Of

Summary In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems introduced in the article [9] and the article [11] to the proof. Using the definition of the article [10], we also proved some theorems on bounded functions.

scholarly journals VI. On the general theory integration

1905 ◽  
Vol 204 (372-386) ◽  
pp. 221-252 ◽  
Keyword(s):  
Arbitrary Point ◽  
Continuous Functions ◽  
Common Value ◽  
Theory Integration ◽  
Positive Quantity ◽  
The Common ◽  
Definition Of ◽  
Special Case ◽  
Ordinary Integral ◽  
Definite Limit

Riemann was the first to consider the theory of integration of non-continuous functions. As is well known, his definition of the integral of a function between the limits a and b is as follows:— Divide the segment ( a, b ) into any finite number of intervals, each less, say, than a positive quantity, or norm d ; take the product of each such interval by the value of the function at any point of that interval, and form the sum of all these products; if this sum has a limit, when d is indefinitely diminished which is independent of the mode of division into intervals, and of the choice of the points in those intervals at which the values of the function are considered, this limit is called the integral of the function from a to b . The most convenient mode, however, of defining a Riemann (that is an ordinary) integral of a function, is due to Darboux; it is based on the introduction of upper and lower integrals (intégrale par excès, par défaut: oberes, unteres Integral). The definitions of these are as follows:— It may be shown that, if the interval ( a, b ) be divided as before, and the sum of the products taken as before, but with this difference, that instead of the value of the function at an arbitrary point of the part, the upper (lower) limit of the values of the function in the part be taken and multiplied by the length of the corresponding part, these summations have, whatever he the type of function, each of them a definite limit, independent of the mode of division and the mode in which d approaches the value zero. This limit is called the upper (lower) integral of the function. In the special case in which these two limits agree, the common value is called the integral the function .

scholarly journals Functional Space Consisted by Continuous Functions on Topological Space

2021 ◽  
Vol 29 (1) ◽  
pp. 49-62
Author(s):  
Hiroshi Yamazaki ◽  
Keiichi Miyajima ◽  
Yasunari Shidama
Keyword(s):  
Banach Space ◽  
Topological Space ◽  
Function Space ◽  
Normed Space ◽  
Functional Space ◽  
Continuous Functions ◽  
Bounded Support ◽  
Compact Topological Space ◽  
Definition Of ◽  
System 1

Summary In this article, using the Mizar system [1], [2], first we give a definition of a functional space which is constructed from all continuous functions defined on a compact topological space [5]. We prove that this functional space is a Banach space [3]. Next, we give a definition of a function space which is constructed from all continuous functions with bounded support. We also prove that this function space is a normed space.

Strictly singular and strictly cosingular operators on spaces of continuous functions

1991 ◽  
Vol 110 (3) ◽  
pp. 505-521 ◽  
Author(s):  
Catherine Abbott ◽  
Elizabeth Bator ◽  
Paul Lewis
Keyword(s):  
Banach Space ◽  
Continuous Function ◽  
Banach Spaces ◽  
Borel Subset ◽  
Continuous Functions ◽  
Alternative Solution ◽  
Representing Measure ◽  
Extension Theorems ◽  
Spaces Of Continuous Functions ◽  
Strictly Singular

In this paper we will be concerned with studying operators T: C(K, X) → Y defined on Banach spaces of continuous functions. We will be particularly interested in studying the classes of strictly singular and strictly cosingular operators. In the process, we obtain answers to certain questions recently raised by Bombal and Porras in [5]. Specifically, we study Banach space X and Y for which an operator T: C(K, X) → Y with representing measure m is strictly singular (strictly cosingular) whenever m is strongly bounded and m(A) is strictly singular (strictly cosingular) for each Borel subset A of K. Along the way we establish several results dealing with non-compact operators on continuous function spaces, and we consolidate numerous results concerning extension theorems for operators defined on these same spaces. Also, we join Saab and Saab [25] in demonstrating that if l1 does not embed in X* then the adjoint T* of a strongly bounded map must be weakly precompact, thereby presenting an alternative solution to a question raised in [2].

TOPOLOGICAL CHAOS FOR A CLASS OF LINEAR MODELS

1992 ◽  
Vol 02 (01) ◽  
pp. 79-90 ◽  
Author(s):  
V. PROTOPOPESCU ◽  
Y.Y. AZMY
Keyword(s):  
Banach Space ◽  
Linear Models ◽  
Shift Operator ◽  
Topological Transitivity ◽  
Linear Rate ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Topological Chaos ◽  
Backward Shift ◽  
The Relationship

We construct an example of linear rate equation in the Banach space of summable sequences, l1, that exhibits the three properties required as signature of topological chaos, namely: (i) topological transitivity, (ii) dense periodic orbits, and (iii) positive Lyapunov exponents. The example is based on the properties of the backward shift operator on the Banach space l1. Since linear chaos in the sense described above can occur only in an infinite-dimensional setting, possible finite-dimensional approximate manifestations are investigated. The relationship between the linear backward shift and the nonlinear Bernoulli shift is also discussed.

Projections in the Convex Hull of Surjective Isometries

2010 ◽  
Vol 53 (3) ◽  
pp. 398-403 ◽  
Author(s):  
Fernanda Botelho ◽  
James Jamison
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Banach Spaces ◽  
Convex Combination ◽  
Continuous Functions ◽  
Convex Banach Space ◽  
Strictly Convex ◽  
Strictly Convex Banach Space ◽  
Spaces Of Continuous Functions

AbstractWe characterize those linear projections represented as a convex combination of two surjective isometries on standard Banach spaces of continuous functions with values in a strictly convex Banach space.

scholarly journals An approximative property of spaces of continuous functions

1974 ◽  
Vol 15 (1) ◽  
pp. 48-53 ◽  
Author(s):  
R. B. Holmes ◽  
J. D. Ward
Keyword(s):  
Banach Space ◽  
Closed Subspace ◽  
Continuous Functions ◽  
Compact Set ◽  
Canonical Embedding ◽  
Locally Compact ◽  
Nearest Point ◽  
Spaces Of Continuous Functions ◽  
Approximative Property ◽  
Canonical Image

A Banach space X is said to have property (PROXBID) if the canonical image of X in its bidual X** is proximal. In other words, if J: X → X** is the canonical embedding, then it is required that every element of X** have at least one best approximation (i.e., nearest point) from the closed subspace J(X). We show below that, if X is the space of (real or complex) continuous functions on a compact set, or the space of (real or complex) continuous functions that vanish at infinity on a locally compact set, then X has property (PROXBID). At this point we should mention the existence of a variety of examples [2, 8] of Banach spaces which lack property (PROXBID).

SIMILARITIES AND DIFFERENT FEATURES OF HAND GESTURES IN AMERICAN AND KYRGYZ CULTURES

2019 ◽  
pp. 19-22
Author(s):  
Avtandil kyzy Ya
Keyword(s):  
Everyday Life ◽  
Facial Expressions ◽  
Main Part ◽  
Body Language ◽  
Hand Gestures ◽  
Common Definition ◽  
The World ◽  
The Common ◽  
Definition Of ◽  
Different Cultures

Abstract: This paper highlights similarities and different features of the category of kinesics “hand gestures”, its frequency usage and acceptance by different individuals in two different cultures. This study shows its similarities, differences and importance of the gestures, for people in both cultures. Consequently, kinesics study was mentioned as a main part of body language. As indicated in the article, the study kinesics was not presented in the Kyrgyz culture well enough, though Kyrgyz people use hand gestures a lot in their everyday life. The research paper begins with the common definition of hand gestures as a part of body language, several handshake categories like: the finger squeeze, the limp fish, the two-handed handshake were explained by several statements in the English and Kyrgyz languages. Furthermore, this article includes definitions and some idioms containing hand, shake, squeeze according to the Oxford and Academic Dictionary to show readers the figurative meanings of these common words. The current study was based on the books of writers Allan and Barbara Pease “The definite book of body language” 2004, Romana Lefevre “Rude hand gestures of the world”2011 etc. Key words: kinesics, body language, gestures, acoustics, applause, paralanguage, non-verbal communication, finger squeeze, perceptions, facial expressions. Аннотация. Бул макалада вербалдык эмес сүйлѳшүүнүн бѳлүгү болуп эсептелген “колдордун жандоо кыймылы”, алардын эки башка маданиятта колдонулушу, айырмачылыгы жана окшош жактары каралган. Макаланын максаты болуп “колдордун жандоо кыймылынын” мааниси, айырмасы жана эки маданиятта колдонулушу эсептелет. Ошону менен бирге, вербалдык эмес сүйлѳшүүнүн бѳлүгү болуп эсептелген “кинесика” илими каралган. Берилген макалада кѳрсѳтүлгѳндѳй, “кинесика” илими кыргыз маданиятында толугу менен изилденген эмес, ошого карабастан “кинесика” илиминин бѳлүгү болуп эсептелген “колдордун жандоо кыймылы” кыргыз элинин маданиятында кѳп колдонулат. Андан тышкары, “колдордун жандоо кыймылынын” бир нече түрү, англис жана кыргыз тилдеринде ма- селен аркылуу берилген.Тѳмѳнкү изилдѳѳ ишин жазууда чет элдик жазуучулардын эмгектери колдонулду. Түйүндүү сѳздѳр: кинесика, жандоо кыймылы, акустика,кол чабуулар, паралингвистика, вербалдык эмес баарлашуу,кол кысуу,кабыл алуу сезими. Аннотация. В данной статье рассматриваются сходства и различия “жестикуляции” и частота ее использования, в американской и кыргызской культурах. Следовательно, здесь было упомянуто понятие “кинесика” как основная часть языка тела. Как указано в статье, “кинесика” не была представлена в кыргызской культуре достаточно хорошо, хотя кыргызский народ часто использует жестикуляцию в повседневной жизни. Исследовательская работа начинается с общего определения “жестикуляции” как части языка тела и несколько категорий жестикуляции, таких как: сжатие пальца, слабое рукопожатие, рукопожатие двумя руками, были объяснены несколькими примерами на английском и кыргызском языках. Кроме того, эта статья включает определения слов “рука”, “рукопожатие”, “сжатие” и некоторые идиомы, содержащие данных слов согласно Оксфордскому и Академическому словарю, чтобы показать читателям их образное значение. Данное исследование было основано на книгах писателей Аллана и Барбары Пиз «Определенная книга языка тела» 2004 года, Романа Лефевра «Грубые жестикуляции мира» 2011 года и т.д. Ключевые слова: кинесика, язык жестов, жесты, акустика, аплодисменты, паралингвистика, невербальная коммуникация, сжатие пальца, чувство восприятия, выражение лиц.

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