On the relationship between ? p -Radonifying operators and other operator ideals in Banach spaces of stable typep

1988 ◽  
Vol 281 (1) ◽  
pp. 145-156
Author(s):  
Yasuji Takahashi ◽  
Yoshiaki Okazaki
Keyword(s):  
Banach Spaces ◽  
Operator Ideals ◽  
The Relationship

Injective Dual Banach Spaces and Operator Ideals

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Raffaella Cilia ◽  
Joaquín M. Gutiérrez
Keyword(s):  
Banach Spaces ◽  
Operator Ideals

Duality of the distance to closed operator ideals

2003 ◽  
Vol 133 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Banach Spaces ◽  
Closed Operator ◽  
Operator Ideal ◽  
Linear Operators ◽  
Distance Functions ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Special Operator

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

scholarly journals Primal Lower Nice Functions in Reflexive Smooth Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2066
Author(s):  
Messaoud Bounkhel ◽  
Mostafa Bachar
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Space Setting ◽  
Nonlinear Anal ◽  
Finite Dimensional ◽  
In Trans ◽  
First Time ◽  
The Relationship ◽  
Primal Lower Nice Functions

In the present work, we extend, to the setting of reflexive smooth Banach spaces, the class of primal lower nice functions, which was proposed, for the first time, in finite dimensional spaces in [Nonlinear Anal. 1991, 17, 385–398] and enlarged to Hilbert spaces in [Trans. Am. Math. Soc. 1995, 347, 1269–1294]. Our principal target is to extend some existing characterisations of this class to our Banach space setting and to study the relationship between this concept and the generalised V-prox-regularity of the epigraphs in the sense proposed recently by the authors in [J. Math. Anal. Appl. 2019, 475, 699–29].

scholarly journals The history of a general criterium on spaceability

2017 ◽  
Vol 15 (1) ◽  
pp. 252-260
Author(s):  
Víctor M. Sánchez
Keyword(s):  
Banach Spaces ◽  
Operator Ideals ◽  
Survey Paper ◽  
Arbitrary Operator ◽  
History Of

Abstract There are just a few general criteria on spaceability. This survey paper is the history of one of the first ones. Let I1 and I2 be arbitrary operator ideals and E and F be Banach spaces. The spaceability of the set of operators I1(E, F)\ I2(E, F) is studied. Before stating the criterium, the paper summarizes the main results about lineability and spaceability of differences between particular operator ideals obtained in recent years. They are the seed of the ideas contained in the general criterium.

scholarly journals On symmetric ideals of multilinear mappings between Banach spaces

2006 ◽  
Vol 81 (1) ◽  
pp. 141-148 ◽  
Author(s):  
Geraldo Botelho ◽  
Daniel M. Pellegrino
Keyword(s):  
Banach Spaces ◽  
Operator Ideals ◽  
Multilinear Mappings

AbstractIn this paper we provide examples and counterexamples of symmetric ideals of multilinear mappings between Banach spaces and prove that if I1, …, In are operator ideals, then the ideals of multilinear mappings L(I1, …, In) and /I1, …, In/ are symmetric if and only if I1 = … = In.

SIP Xd-frames and their perturbations in uniformly convex Banach spaces

2014 ◽  
Vol 12 (03) ◽  
pp. 1450024
Author(s):  
Xianwei Zheng ◽  
Shouzhi Yang
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Inner Product ◽  
Uniformly Convex ◽  
Atomic Decompositions ◽  
Banach Frames ◽  
Uniformly Convex Banach Spaces ◽  
Bk Space ◽  
The Relationship

In this paper, we introduce the definitions of SIP-I and SIP-II Xd-frames in a uniformly convex, separable Banach space X with respect to a BK-space Xd (here SIP represents semi-inner product), both of them are defined as sequence of elements in X. We characterize SIP-I and SIP-II Xd-frames in terms of the corresponding synthesis and analysis operators, respectively, then we consider perturbations for both of them. Furthermore, we also introduce the definitions of SIP Banach frames and SIP atomic decompositions. Under certain assumptions, we establish the relationship between SIP Banach frames and SIP atomic decompositions, and therefore obtain reconstruction formulas for every element in X and X* by using a pair of SIP-I and SIP-II Xd-frames for X. Finally, we discuss perturbations of SIP Banach frames and SIP atomic decompositions.

23.—Weak Continuity Properties of Mappings and Semigroups

1975 ◽  
Vol 72 (4) ◽  
pp. 275-280 ◽  
Author(s):  
J. M. Ball
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Weak Continuity ◽  
Continuity Properties ◽  
The Relationship

SynopsisThe relationship between weak and sequential weak continuity for mappings between Banach spaces and semigroups on Banach space is studied.

scholarly journals UNIVERSAL SUBGROUPS OF POLISH GROUPS

2014 ◽  
Vol 79 (4) ◽  
pp. 1148-1183 ◽  
Author(s):  
KONSTANTINOS A. BEROS
Keyword(s):  
Topological Group ◽  
Banach Spaces ◽  
Topological Groups ◽  
Locally Compact ◽  
Polish Groups ◽  
Countable Power ◽  
Compact Case ◽  
Image Position ◽  
The Relationship ◽  
Compactly Generated

AbstractGiven a class${\cal C}$of subgroups of a topological groupG, we say that a subgroup$H \in {\cal C}$is auniversal${\cal C}$subgroupofGif every subgroup$K \in {\cal C}$is a continuous homomorphic preimage ofH. Such subgroups may be regarded as complete members of${\cal C}$with respect to a natural preorder on the set of subgroups ofG. We show that for any locally compact Polish groupG, the countable powerGωhas a universalKσsubgroup and a universal compactly generated subgroup. We prove a weaker version of this in the nonlocally compact case and provide an example showing that this result cannot readily be improved. Additionally, we show that many standard Banach spaces (viewed as additive topological groups) have universalKσand compactly generated subgroups. As an aside, we explore the relationship between the classes ofKσand compactly generated subgroups and give conditions under which the two coincide.

Sign in / Sign up

Export Citation Format

Share Document