Quasinormability of Vector Valued Sequence Spaces

2019 ◽  
pp. 21-28
Author(s):  
Fernando Blasco
Keyword(s):  
Sequence Spaces ◽  
Vector Valued

Entropy numbers of operators acting between vector-valued sequence spaces

2012 ◽  
Vol 286 (5-6) ◽  
pp. 614-630 ◽  
Author(s):  
David E. Edmunds ◽  
Yuri Netrusov
Keyword(s):  
Sequence Spaces ◽  
Entropy Numbers ◽  
Vector Valued

Some vector valued sequence spaces of Musielak-Orlicz functions and their operator ideals

2018 ◽  
Vol 68 (1) ◽  
pp. 115-134 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Kuldip Raj
Keyword(s):  
Sequence Space ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Orlicz Sequence Space ◽  
Geometric Properties ◽  
Orlicz Functions ◽  
Opial Property ◽  
Uniform Opial Property ◽  
Vector Valued

AbstractIn the present paper we introduce generalized vector-valued Musielak-Orlicz sequence spacel(A,𝓜,u,p,Δr,∥·,… ,·∥)(X) and study some geometric properties like uniformly monotone, uniform Opial property for this space. Further, we discuss the operators ofs-type and operator ideals by using the sequence ofs-number (in the sense of Pietsch) under certain conditions on matrixA.

scholarly journals Strongly Summable Vector-Valued Sequence Spaces Defined by 2-modular

CAUCHY ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 279-285
Author(s):  
Burhanudin Arif Nurnugroho ◽  
Puguh Wahyu Prasetyo
Keyword(s):  
Sequence Spaces ◽  
Modular Space ◽  
Important Concept ◽  
Vector Valued

Summability is an important concept in sequence spaces. One summability concept is strongly Cesaro summable. In this paper, we study a subset of the set of all vector-valued sequence in 2-modular space. Some facts that we investigated in this paper include linearity, the existence of modular and completeness with respect to these modular.

Rotundity In Köthe Spaces of Vector-Valued Functions

1989 ◽  
Vol 41 (4) ◽  
pp. 659-675 ◽  
Author(s):  
A. Kamińska ◽  
B. Turett
Keyword(s):  
Banach Space ◽  
Analogous Result ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Uniform Rotundity ◽  
Köthe Spaces ◽  
Bochner Space ◽  
Köthe Space ◽  
Vector Valued Functions ◽  
Vector Valued

In this paper, Köthe spaces of vector-valued functions are considered. These spaces, which are generalizations of both the Lebesgue-Bochner and Orlicz-Bochner spaces, have been studied by several people (e.g., see [1], [8]). Perhaps the earliest paper concerning the rotundity of such Köthe space is due to I. Halperin [8]. In his paper, Halperin proved that the function spaces E(X) is uniformly rotund exactly when both the Köthe space E and the Banach space X are uniformly rotund; this generalized the analogous result, due to M. M. Day [4], concerning Lebesgue-Bochner spaces. In [20], M. Smith and B. Turett showed that many properties akin to uniform rotundity lift from X to the Lebesgue-Bochner space LP(X) when 1 < p < ∞. A survey of rotundity notions in Lebesgue-Bochner function and sequence spaces can be found in [19].

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