scholarly journals Interpolating sequence on certain Banach spaces of analytic functions

2002 ◽  
Vol 65 (2) ◽  
pp. 177-182 ◽  
Author(s):  
B. Yousefi
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Connected Domain ◽  
Analytic Functions ◽  
Reflexive Banach Space ◽  
Bounded Operator ◽  
Interpolating Sequence ◽  
Spaces Of Analytic Functions

Let G be a finitely connected domain and let X be a reflexive Banach space of functions analytic on G which admits the multiplication Mz as a polynomially bounded operator. We give some conditions that a sequence in G has an interpolating subsequence for X.

Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

1999 ◽  
Vol 42 (2) ◽  
pp. 139-148 ◽  
Author(s):  
José Bonet ◽  
Paweł Dománski ◽  
Mikael Lindström
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weak Compactness ◽  
Weakly Compact ◽  
Point Evaluation ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractEvery weakly compact composition operator between weighted Banach spaces of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

scholarly journals Extensions of the classical Cesaro operator on Hardy spaces

2011 ◽  
Vol 108 (2) ◽  
pp. 279 ◽  
Author(s):  
Guillermo P. Curbera ◽  
Werner J. Ricker
Keyword(s):  
Banach Space ◽  
Hardy Space ◽  
Banach Spaces ◽  
Hardy Spaces ◽  
Analytic Functions ◽  
Cesàro Operator ◽  
Cesaro Operator ◽  
Spaces Of Analytic Functions

For each $1\le p<\infty$, the classical Cesàro operator $\mathcal C$ from the Hardy space $H^p$ to itself has the property that there exist analytic functions $f\notin H^p$ with ${\mathcal C}(f)\in H^p$. This article deals with the identification and properties of the (Banach) space $[{\mathcal C}, H^p]$ consisting of all analytic functions that $\mathcal C$ maps into $H^p$. It is shown that $[{\mathcal C}, H^p]$ contains classical Banach spaces of analytic functions $X$, genuinely bigger that $H^p$, such that $\mathcal C$ has a continuous $H^p$-valued extension to $X$. An important feature is that $[{\mathcal C}, H^p]$ is the largest amongst all such spaces $X$.

scholarly journals Operators acting on certain Banach spaces of analytic functions

1995 ◽  
Vol 18 (1) ◽  
pp. 107-110 ◽  
Author(s):  
K. Seddighi ◽  
K. Hedayatiyan ◽  
B. Yousefi
Keyword(s):  
Banach Space ◽  
Reflexive Banach Space ◽  
Bounded Operator ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Plane Domain ◽  
Multiplication Operators ◽  
Independent Variable ◽  
Spaces Of Analytic Functions ◽  
Analytic Plane

Let𝒳be reflexive Banach space of functions analytic plane domainΩsuch that for everyλinΩthe functional of evaluation atλis bounded. Assume further that𝒳contains the constants andMzmultiplication by the independent variablez, is bounded operator on𝒳. We give sufficient conditions forMzto be reflexive. In particular, we prove that the operatorsMzonEP(Ω)and certainHaP(β)reflexive. We also prove that the algebra of multiplication operators on Bergman spaces is reflexive, giving simpler proof of result of Eschmeier.

scholarly journals Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 150
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Entire Functions ◽  
Dimensional Algebra ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Linear Subspaces ◽  
Infinite Dimensional Banach Space

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.

Projections on Tree-Like banach Spaces

1985 ◽  
Vol 37 (5) ◽  
pp. 908-920
Author(s):  
A. D. Andrew
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Unconditional Basis ◽  
Reflexive Banach Space ◽  
Separable Space ◽  
Bounded Linear ◽  
Tree Space

1. In this paper, we investigate the ranges of projections on certain Banach spaces of functions defined on a diadic tree. The notion of a “tree-like” Banach space is due to James 4], who used it to construct the separable space JT which has nonseparable dual and yet does not contain l1. This idea has proved useful. In [3], Hagler constructed a hereditarily c0 tree space, HT, and Schechtman [6] constructed, for each 1 ≦ p ≦ ∞, a reflexive Banach space, STp with a 1-unconditional basis which does not contain lp yet is uniformly isomorphic to for each n.In [1] we showed that if U is a bounded linear operator on JT, then there exists a subspace W ⊂ JT, isomorphic to JT such that either U or (1 — U) acts as an isomorphism on W and UW or (1 — U)W is complemented in JT. In this paper, we establish this result for the Hagler and Schechtman tree spaces.

scholarly journals Almost Surjective Epsilon-Isometry in The Reflexive Banach Spaces

CAUCHY ◽  
2017 ◽  
Vol 4 (4) ◽  
pp. 167
Author(s):  
Minanur Rohman
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Lorentz Space ◽  
Bounded Linear Operator ◽  
Closed Subspace ◽  
Reflexive Banach Space ◽  
Reflexive Banach Spaces ◽  
Bounded Linear ◽  
Star Topology

<p class="AbstractCxSpFirst">In this paper, we will discuss some applications of almost surjective epsilon-isometry mapping, one of them is in Lorentz space ( L_(p,q)-space). Furthermore, using some classical theorems of w star-topology and concept of closed subspace -complemented, for every almost surjective epsilon-isometry mapping  <em>f </em>: <em>X to</em><em> Y</em>, where <em>Y</em> is a reflexive Banach space, then there exists a bounded linear operator   <em>T</em> : <em>Y to</em><em> X</em>  with  such that</p><p class="AbstractCxSpMiddle">  </p><p class="AbstractCxSpLast">for every x in X.</p>

scholarly journals Hermitian operators and isometries on sums of Banach spaces

1989 ◽  
Vol 32 (2) ◽  
pp. 169-191 ◽  
Author(s):  
R. J. Fleming ◽  
J. E. Jamison
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sequence Space ◽  
Reflexive Banach Space ◽  
Geometric Theory ◽  
Orlicz Sequence Space ◽  
Vector Sequence ◽  
Banach Sequence Space ◽  
Banach Sequence

Let E be a Banach sequence space with the property that if (αi) ∈ E and |βi|≦|αi| for all i then (βi) ∈ E and ‖(βi)‖E≦‖(αi)‖E. For example E could be co, lp or some Orlicz sequence space. If (Xn) is a sequence of real or complex Banach spaces, then E can be used to construct a vector sequence space which we will call the E sum of the Xn's and symbolize by ⊕EXn. Specifically, ⊕EXn = {(xn)|(xn)∈Xn and (‖xn‖)∈E}. The E sum is a Banach space with norm defined by: ‖(xn)‖ = ‖(‖xn‖)‖E. This type of space has long been the source of examples and counter-examples in the geometric theory of Banach spaces. For instance, Day [7] used E=lp and Xk=lqk, with appropriate choice of qk, to give an example of a reflexive Banach space not isomorphic to any uniformly conves Banach space. Recently VanDulst and Devalk [33] have considered Orlicz sums of Banach spaces in their studies of Kadec-Klee property.

scholarly journals Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 133
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Main Question ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
Taylor Polynomials

In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space X. The main question is: under which conditions is there an analytic function of unbounded type on X such that its Taylor polynomials are in prescribed subspaces of polynomials? We obtain some sufficient conditions for a function f to be of unbounded type and show that there are various subalgebras of polynomials that support analytic functions of unbounded type. In particular, some examples of symmetric analytic functions of unbounded type are constructed.

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