scholarly journals The Near Subnormal Weighted Shift and Recursiveness

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
R. Ben Taher ◽  
M. Rachidi
Keyword(s):  
Finite Order ◽  
Weighted Shift ◽  
Necessary Condition ◽  
Important Class ◽  
Weighted Shifts ◽  
Basic Properties ◽  
Recursive Sequences ◽  
Recursive Relations

We aim at studying the near subnormality of the unilateral weighted shifts, whose moment sequences are defined by linear recursive relations of finite order. Using the basic properties of recursive sequences, we provide a natural necessary condition, that ensure the near subnormality of this important class of weighted shifs. Some related new results are established; moreover, applications and consequences are presented; notably the notion of near subnormal completion weighted shift is implanted and explored.

Chaos for Cosine Operator Functions Generated by Shifts

2014 ◽  
Vol 24 (09) ◽  
pp. 1450108 ◽  
Author(s):  
Chung-Chuan Chen
Keyword(s):  
Operator Function ◽  
Weighted Shift ◽  
Necessary Condition ◽  
Weighted Shifts ◽  
Cosine Operator Function ◽  
Cosine Operator ◽  
Operator Functions ◽  
Cosine Operator Functions ◽  
Sufficient And Necessary Condition

Let 1 ≤ p < ∞. We give the sufficient and necessary condition for cosine operator functions, generated by bilateral weighted shifts on ℓp(ℤ), to be chaotic. Moreover, such a cosine operator function is chaotic if, and only if, its weighted shift is chaotic.

DISINTEGRATION-OF-MEASURE TECHNIQUES FOR COMMUTING MULTIVARIABLE WEIGHTED SHIFTS

2006 ◽  
Vol 92 (2) ◽  
pp. 381-402 ◽  
Author(s):  
RAÚL E. CURTO ◽  
JASANG YOON
Keyword(s):  
Weighted Shift ◽  
Necessary Condition ◽  
Weighted Shifts ◽  
Disintegration Of Measures

We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting $n$-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal $2$-variable weighted shifts, we then find the precise relation between the Berger measure of the pair and the Berger measures of the shifts associated to horizontal rows and vertical columns of weights.

scholarly journals On t-Neighbourhoods in Trigonometric Topological Spaces

2021 ◽  
Vol 12 (1S) ◽  
pp. 655-658
Author(s):  
S. Malathi, Et. al.
Keyword(s):  
Necessary Condition ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Type ◽  
The Relationship

In this paper we introduce a new type of neighbourhoods, namely, t-neighbourhoods in trigonometric topological spaces and study their basic properties. Also, we discuss the relationship between neighbourhoods and t-neighbourhoods. Further, we give the necessary condition for t-neighbourhoods in trigonometric topological spaces.  .

On the Unicellularity of Weighted Shifts

1971 ◽  
Vol 12 (3) ◽  
pp. 342-350 ◽  
Author(s):  
K. J. Harrison
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Ordered Set ◽  
Invariant Subspaces ◽  
Weighted Shift ◽  
Weighted Shifts ◽  
Totally Ordered Set

An operator acting on a Banach space is said to be unicellular if its lattice of invariant subspaces is totally ordered by inclusion. Each weighted shift on a sequence space has a natural totally ordered set of invariant subspaces, and is unicellular if these are its only invariant subspaces.

BACKWARD 3-STEP EXTENSIONS OF RECURSIVELY GENERATED WEIGHTED SHIFTS: A RANGE OF QUADRATIC HYPONORMALITY

2013 ◽  
Vol 89 (3) ◽  
pp. 488-493
Author(s):  
GEORGE R. EXNER ◽  
IL BONG JUNG ◽  
MI RYEONG LEE ◽  
SUN HYUN PARK
Keyword(s):  
Open Problem ◽  
Weighted Shift ◽  
Real Numbers ◽  
Weighted Shifts ◽  
Positive Real ◽  
Weight Sequence ◽  
Weighted Sequence ◽  
Quadratically Hyponormal

AbstractLet $\alpha : 1, 1, \sqrt{x} , \mathop{( \sqrt{u} , \sqrt{v} , \sqrt{w} )}\nolimits ^{\wedge } $ be a backward 3-step extension of a recursively generated weighted sequence of positive real numbers with $1\leq x\leq u\leq v\leq w$ and let ${W}_{\alpha } $ be the associated weighted shift with weight sequence $\alpha $. The set of positive real numbers $x$ such that ${W}_{\alpha } $ is quadratically hyponormal for some $u, v$ and $w$ is described, solving an open problem due to Curto and Jung [‘Quadratically hyponormal weighted shifts with two equal weights’, Integr. Equ. Oper. Theory 37 (2000), 208–231].

To the Mathematical Concept of Thermostatics To the Mathematical Concept of Thermostatics

1982 ◽  
Vol 37 (1) ◽  
pp. 1-5
Author(s):  
A. Grauel
Keyword(s):  
Mathematical Concept ◽  
Necessary Condition ◽  
Second Law ◽  
Field Equations ◽  
Basic Properties ◽  
Integrating Factor

Abstract We discuss the integrated form of the laws of thermostatics by using Stokes theorem on manifolds. We give a new insight to the basic properties of thermostatics, in particular we show that only the second law is a necessary condition to identify the integrating factor with the temperature. Moreover we consider the thermodynamical field equations for discontinuous media and discuss the properties of thermostatics.

scholarly journals A note on strictly cyclic Shifts onℓp

1978 ◽  
Vol 1 (2) ◽  
pp. 203-208 ◽  
Author(s):  
Gerd H. Fricke
Keyword(s):  
Weighted Shift ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Cyclic Shifts

In this paper the author shows that a well known sufficient condition for strict cycliclty of a weighted shift onℓpis not a necessary condition for anypwith1<p<∞.

scholarly journals Chaos and frequent hypercyclicity for weighted shifts

2020 ◽  
pp. 1-37
Author(s):  
STÉPHANE CHARPENTIER ◽  
KARL GROSSE-ERDMANN ◽  
QUENTIN MENET
Keyword(s):  
Difference Sets ◽  
Weighted Shift ◽  
Sequence Spaces ◽  
Hypercyclic Operators ◽  
Weighted Shifts ◽  
Banach Sequence Spaces ◽  
Frequently Hypercyclic Operators ◽  
Köthe Sequence Spaces ◽  
The Relationship ◽  
Banach Sequence

Abstract Bayart and Ruzsa [Difference sets and frequently hypercyclic weighted shifts. Ergod. Th. & Dynam. Sys.35 (2015), 691–709] have recently shown that every frequently hypercyclic weighted shift on $\ell ^p$ is chaotic. This contrasts with an earlier result of Bayart and Grivaux [Frequently hypercyclic operators. Trans. Amer. Math. Soc.358 (2006), 5083–5117], who constructed a non-chaotic frequently hypercyclic weighted shift on $c_0$ . We first generalize the Bayart–Ruzsa theorem to all Banach sequence spaces in which the unit sequences form a boundedly complete unconditional basis. We then study the relationship between frequent hypercyclicity and chaos for weighted shifts on Fréchet sequence spaces, in particular, on Köthe sequence spaces, and then on the special class of power series spaces. We obtain, rather curiously, that every frequently hypercyclic weighted shift on $H(\mathbb {D})$ is chaotic, while $H(\mathbb {C})$ admits a non-chaotic frequently hypercyclic weighted shift.

The positive properties of isolic integers

1972 ◽  
Vol 37 (1) ◽  
pp. 114-132 ◽  
Author(s):  
Erik Ellentuck
Keyword(s):  
Fundamental Lemma ◽  
Basic Properties ◽  
Skolem Functions ◽  
Arithmetic Hierarchy ◽  
Positive Properties ◽  
Basic Induction ◽  
Recursive Relations ◽  
The Way

In this paper we show (cf. Theorem 22) that in a language L* with equality, whose relation symbols denote arbitrary relations over ω* (=rational integers) and whose function symbols denote (= ∃∀ definable in the arithmetic hierarchy) functions over ω*, (i) a positive sentence is true in Λ* (= isolic integers) iff some Horn reduct is true in ω* with Skolem functions. We also show (cf Theorem 20) that (ii) a universally quantified sentence is true in Λ* iff some Horn reduct is true in Λ*.The latter result is nontrivial because our relations are arbitrary and our functions are In order to obtain (i) it was necessary to generalize the frame extensions of [7]. This is done in §2. Our extension procedure agrees with that of [7] for recursive relations (cf. Theorem 12), and is certainly more general for − relations. What happens in the case is still open. In §3 we develop the basic properties of our extension so that in §4 we can prove a metatheorem (cf. Theorems 8 and 10) about Λ (=isols), in a language L with equality whose relation symbols denote arbitrary relations over ω (=nonnegative integers) and whose function symbols denote almost R↑ combinatorial functions. In Theorem 11 this is generalized to infinitary universal sentences. In §5 generic isols are introduced. These are used (cf. Theorems 16–19) to generalize and simplify the “fundamental lemma” of [8]. The basic induction is patterned after Lemma 4.1 of [8], but is stronger in that any sufficiently generic assignment attainable from a frame yields Skolem functions. Finally in §6 these results are applied to Λ*, yielding the titled result (i) of our paper. Immediately following Theorem 15 there is a discussion which attempts to justify the way we extend relations to Λ.

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