scholarly journals Spectral operators and weakly compact homomorphisms in a class of Banach Spaces

1986 ◽  
Vol 28 (2) ◽  
pp. 215-222 ◽  
Author(s):  
W. Ricker
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Finite Type ◽  
Continuous Linear Operator ◽  
Multiplication Operators ◽  
Continuous Linear ◽  
Simple Application ◽  
Spectral Operator ◽  
Weakly Compact ◽  
Finite Spectrum

The purpose of this note is to present certain aspects of the theory of spectral operators in Grothendieck spaces with the Dunford-Pettis property, briefly, GDP-spaces, thereby elaborating on the recent note [10].For example, the sum and product of commuting spectral operators in such spaces are again spectral operators (cf. Proposition 2.1) and a continuous linear operator is spectral if and only if it has finite spectrum (cf. Proposition 2.2). Accordingly, if a spectral operator is of finite type, then its spectrum consists entirely of eigenvalues. Furthermore, it turns out that there are no unbounded spectral operators in such spaces (cf. Proposition 2.4). As a simple application of these results we are able to determine which multiplication operators in certain function spaces are spectral operators.

scholarly journals OPERATORS ON C0(L,X) WHOSE RANGE DOES NOT CONTAIN c0

2008 ◽  
Vol 77 (3) ◽  
pp. 515-520
Author(s):  
JARNO TALPONEN
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Hausdorff Space ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Locally Compact ◽  
Weakly Compact ◽  
Isolated Points ◽  
Locally Compact Hausdorff Space

AbstractThis paper contains two results: (a) if $\mathrm {X}\neq \{0\}$ is a Banach space and (L,τ) is a nonempty locally compact Hausdorff space without isolated points, then each linear operator T:C0(L,X)→C0(L,X) whose range does not contain an isomorphic copy of c00 satisfies the Daugavet equality $\|\mathbf {I}+T\|=1+\|T\|$; (b) if Γ is a nonempty set and X and Y are Banach spaces such that X is reflexive and Y does not contain c0 isomorphically, then any continuous linear operator T:c0(Γ,X)→Y is weakly compact.

scholarly journals Semi-embeddings of Banach spaces which are hereditarily c0

1983 ◽  
Vol 26 (2) ◽  
pp. 163-167 ◽  
Author(s):  
L. Drewnowski
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Vector Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Continuous Linear Operator ◽  
Closed Unit Ball ◽  
Continuous Linear ◽  
Scattered Space ◽  
Complete Set

Following Lotz, Peck and Porta [9], a continuous linear operator from one Banach space into another is called a semi-embedding if it is one-to-one and maps the closed unit ball of the domain onto a closed (hence complete) set. (Below we shall allow the codomain to be an F-space, i.e., a complete metrisable topological vector space.) One of the main results established in [9] is that if X is a compact scattered space, then every semi-embedding of C(X) into another Banach space is an isomorphism ([9], Main Theorem, (a)⇒(b)).

scholarly journals Sufficient conditions for a continuous linear operator to be weakly compact

1972 ◽  
Vol 7 (2) ◽  
pp. 183-190 ◽  
Author(s):  
Joe Howard ◽  
Kenneth Melendez
Keyword(s):  
Linear Operator ◽  
Sufficient Conditions ◽  
Continuous Linear Operator ◽  
Continuous Operator ◽  
Continuous Linear ◽  
Weakly Compact ◽  
Completely Continuous ◽  
Completely Continuous Operator ◽  
Locally Convex

A locally convex topological vector (LCTV) space E is said to have property V (Dieudonné property) if for every complete separated LCTV space F, every unconditionally converging (weakly completely continuous) operator T: E → F is wsakly compact. First, an investigation of the permanence of property V is given. The permanence of the Dieudonné is analogous. Relationships between property V and the Dieudonné property are then given.

scholarly journals Construction of operators with prescribed orbits in Fréchet spaces with a continuous norm

2011 ◽  
Vol 109 (1) ◽  
pp. 147 ◽  
Author(s):  
Angela A. Albanese
Keyword(s):  
Linear Operator ◽  
Banach Spaces ◽  
Continuous Linear Operator ◽  
Fréchet Space ◽  
Fréchet Spaces ◽  
Continuous Linear ◽  
Continuous Norm ◽  
Infinite Dimensional ◽  
Linearly Independent ◽  
Dense Set

Let $X$ be a separable, infinite dimensional real or complex Fréchet space admitting a continuous norm. Let $\{v_n:\ n\geq 1\}$ be a dense set of linearly independent vectors of $X$. We show that there exists a continuous linear operator $T$ on $X$ such that the orbit of $v_1$ under $T$ is exactly the set $\{v_n:\ n\geq 1\}$. Thus, we extend a result of Grivaux for Banach spaces to the setting of non-normable Fréchet spaces with a continuous norm. We also provide some consequences of the main result.

scholarly journals The () Property in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Danyal Soybaş
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Isomorphic Copy ◽  
Weakly Compact ◽  
Geometric Properties ◽  
Bounded Linear ◽  
Real Functions

A Banach space is said to have (D) property if every bounded linear operator is weakly compact for every Banach space whose dual does not contain an isomorphic copy of . Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V∗) property of Pełczyński (and hence every Banach space with (V) property) has (D) property. We show that the space of real functions, which are integrable with respect to a measure with values in a Banach space , has (D) property. We give some other results concerning Banach spaces with (D) property.

EXOTIC LAPLACIANS AND DERIVATIVES OF WHITE NOISE

2011 ◽  
Vol 14 (01) ◽  
pp. 1-14 ◽  
Author(s):  
LUIGI ACCARDI ◽  
UN CIG JI ◽  
KIMIAKI SAITÔ
Keyword(s):  
Linear Operator ◽  
White Noise ◽  
Continuous Linear Operator ◽  
Higher Order ◽  
Continuous Linear ◽  
White Noise Functionals ◽  
Derivatives Of

In this paper, we give a relationship between the exotic Laplacians and the Lévy Laplacians in terms of the higher-order derivatives of white noise by introducing a bijective and continuous linear operator acting on white noise functionals. Moreover, we study a relationship between exotic Laplacians, acting on higher-order singular functionals, each other in terms of the constructed operator.

scholarly journals A note on Dunford-Pettis operators

1987 ◽  
Vol 29 (2) ◽  
pp. 271-273 ◽  
Author(s):  
J. R. Holub
Keyword(s):  
Linear Operator ◽  
Positive Operator ◽  
Continuous Linear Operator ◽  
Positive Operators ◽  
Regular Operator ◽  
Continuous Linear

Talagrand has shown [4, p. 76] that there exists a continuous linear operator from L1[0, 1] to c0 which is not a Dunford-Pettis operator. In contrast to this result, Gretsky and Ostroy [2] have recently proved that every positive operator from L[0, 1] to c0 is a Dunford-Pettis operator, hence that every regular operator between these spaces (i.e. a difference of positive operators) is Dunford-Pettis.

scholarly journals Reiterative Distributional Chaos on Banach Spaces

2019 ◽  
Vol 29 (14) ◽  
pp. 1950201 ◽  
Author(s):  
Antonio Bonilla ◽  
Marko Kostić
Keyword(s):  
Banach Spaces ◽  
Continuous Linear Operator ◽  
Linear Operators ◽  
Nonzero Vector ◽  
Vector Subspace ◽  
Continuous Linear ◽  
Distributional Chaos ◽  
Dynamical Properties ◽  
Definition Of ◽  
Continuous Linear Operators

If we change the upper and lower densities in the definition of distributional chaos of a continuous linear operator on a Banach space [Formula: see text] by the Banach upper and Banach lower densities, respectively, we obtain Li–Yorke chaos. Motivated by this, we introduce the notions of reiterative distributional chaos of types [Formula: see text], [Formula: see text] and [Formula: see text] for continuous linear operators on Banach spaces, which are characterized in terms of the existence of an irregular vector with additional properties. Moreover, we study its relations with other dynamical properties and present the conditions for the existence of a vector subspace [Formula: see text] of [Formula: see text], such that every nonzero vector in [Formula: see text] is both irregular for [Formula: see text] and distributionally near zero for [Formula: see text].

Linearization of a Contractive Homeomorphism

1968 ◽  
Vol 20 ◽  
pp. 1387-1390
Author(s):  
Ludvik Janos
Keyword(s):  
Linear Operator ◽  
Topological Space ◽  
Vector Space ◽  
Topological Vector Space ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Topological Embedding

Let X be a topological space and ϕ: X ⟶ X a continuous self-mapping of X. We say that ϕ is linearized in L by Φ if there exists a topological embedding μ: X ⟶ L of the space X into the linear topological vector space L such that for all x ϵ X, μ (ϕ (x)) = Φ (μ (x)), where ϕ is a continuous linear operator on L.

Bounded continuous linear operator on cone normed space C'[a,b] to C[a,b]

2016 ◽  
Vol 5 ◽  
pp. 65-73
Author(s):  
Sunarsini ◽  
Sadjidon ◽  
Agus Nur Ahmad Syarifudin
Keyword(s):  
Linear Operator ◽  
Normed Space ◽  
Continuous Linear Operator ◽  
Continuous Linear
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