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.

Upper lp-estimates in vector sequence spaces, with some applications

1993 ◽  
Vol 113 (2) ◽  
pp. 329-334 ◽  
Author(s):  
Jesús M. F. Castillo ◽  
Fernando Sánchez
Keyword(s):  
Banach Spaces ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Vector Sequence ◽  
Lp Estimates ◽  
Banach Sequence Space ◽  
Banach Sequence

In [11], Partington proved that if λ is a Banach sequence space with a monotone basis having the Banach-Saks property, and (Xn) is a sequence of Banach spaces each having the Banach-Saks property, then the vector sequence space ΣλXn has this same property. In addition, Partington gave an example showing that if λ and each Xn, have the weak Banach-Saks property, then ΣλXn need not have the weak Banach-Saks property.

scholarly journals Nonwandering operators in Banach space

2005 ◽  
Vol 2005 (24) ◽  
pp. 3895-3908 ◽  
Author(s):  
Lixin Tian ◽  
Jiangbo Zhou ◽  
Xun Liu ◽  
Guangsheng Zhong
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sequence Space ◽  
Separable Banach Space ◽  
Infinite Dimensional ◽  
Banach Sequence Space ◽  
Background Space ◽  
Physical Background ◽  
Structurally Stable ◽  
Banach Sequence

We introduce nonwandering operators in infinite-dimensional separable Banach space. They are new linear chaotic operators and are relative to hypercylic operators, but different from them. Firstly, we show some examples for nonwandering operators in some typical infinite-dimensional Banach spaces, including Banach sequence space and physical background space. Then we present some properties of nonwandering operators and the spectra decomposition of invertible nonwandering operators. Finally, we obtain that invertible nonwandering operators are locally structurally stable.

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 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.

scholarly journals Bregmanf-Projection Operator with Applications to Variational Inequalities in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Chin-Tzong Pang ◽  
Eskandar Naraghirad ◽  
Ching-Feng Wen
Keyword(s):  
Banach Space ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Projection Operator ◽  
Dual Space ◽  
Reflexive Banach Space ◽  
Lower Semicontinuous ◽  
Existence Of A Solution ◽  
Bregman Functions ◽  
Proper Convex

Using Bregman functions, we introduce the new concept of Bregman generalizedf-projection operatorProjCf, g:E*→C, whereEis a reflexive Banach space with dual spaceE*; f: E→ℝ∪+∞is a proper, convex, lower semicontinuous and bounded from below function;g: E→ℝis a strictly convex and Gâteaux differentiable function; andCis a nonempty, closed, and convex subset ofE. The existence of a solution for a class of variational inequalities in Banach spaces is presented.

scholarly journals Quasi-Compactness in Quasi-Banach Spaces

2013 ◽  
Vol 4 (1) ◽  
pp. 325-341
Author(s):  
Raheam A. Mansor Al-Saphory ◽  
Mahmood K Jasim
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Compact Operator ◽  
Sequence Space ◽  
Normed Space ◽  
Sufficient Condition ◽  
Important Extension

Quasi-compactness in a quasi-Banach space for the sequence space Lp, p< 0 < p <1 has been introduced based on the important extension of Milman's reverse Brunn-Minkowiski inequality by Bastero et al. in 1995. Moreover, Many interesting results connected with quasi-compactness and quasi-completeness in a quasi-normed space, Lp for 0 < p < 1 have been explored. Furthermore, we have shown that, the quasi-normed space under  which condition is a quasi Banach space. Also, we have shown that the space if it is quasi-compact in quasi normed space then it is  quasi Banach  space and the converse is not true. Finally, a sufficient condition of the existence for a quasi-compact operator from Lp -> Lp has been presented and analyzed.

scholarly journals A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Kamonrat Nammanee ◽  
Suthep Suantai ◽  
Prasit Cholamjiak
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Reflexive Banach Space ◽  
Duality Mapping ◽  
Nonexpansive Semigroup ◽  
Gauge Functions ◽  
Implicit And Explicit ◽  
General Iterative Method

We study strong convergence of the sequence generated by implicit and explicit general iterative methods for a one-parameter nonexpansive semigroup in a reflexive Banach space which admits the duality mappingJφ, whereφis a gauge function on[0,∞). Our results improve and extend those announced by G. Marino and H.-K. Xu (2006) and many authors.

scholarly journals Ideals of compact operators

2004 ◽  
Vol 77 (1) ◽  
pp. 91-110 ◽  
Author(s):  
Åsvald Lima ◽  
Eve Oja
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Approximation Property ◽  
Closed Subspace ◽  
Reflexive Banach Space ◽  
Compact Operators ◽  
Compact Approximation

AbstractWe give an example of a Banach space X such that K (X, X) is not an ideal in K (X, X**). We prove that if z* is a weak* denting point in the unit ball of Z* and if X is a closed subspace of a Banach space Y, then the set of norm-preserving extensions H B(x* ⊗ z*) ⊆ (Z*, Y)* of a functional x* ⊗ Z* ∈ (Z ⊗ X)* is equal to the set H B(x*) ⊗ {z*}. Using this result, we show that if X is an M-ideal in Y and Z is a reflexive Banach space, then K (Z, X) is an M-ideal in K(Z, Y) whenever K (Z, X) is an ideal in K (Z, Y). We also show that K (Z, X) is an ideal (respectively, an M-ideal) in K (Z, Y) for all Banach spaces Z whenever X is an ideal (respectively, an M-ideal) in Y and X * has the compact approximation property with conjugate operators.

On the Poincaré-Hopf Theorem for Functionals Defined on Banach Spaces

2009 ◽  
Vol 9 (4) ◽  
Author(s):  
Silvia Cingolani ◽  
Marco Degiovanni
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Differentiable Function ◽  
Reflexive Banach Space ◽  
Hopf Theorem

AbstractLet X be a reflexive Banach space and f : X → ℝ a Gâteaux differentiable function with f′ demicontinuous and locally of class (S)

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