scholarly journals Vector valued Orlicz-Lorentz sequence spaces and their operator ideals

2017 ◽  
Vol 10 (02) ◽  
pp. 338-353 ◽  
Author(s):  
S. A. Mohiuddine ◽  
Kuldip Raj
Keyword(s):  
Sequence Spaces ◽  
Operator Ideals ◽  
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.

Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals

2014 ◽  
Vol 64 (6) ◽  
Author(s):  
Manjul Gupta ◽  
Antara Bhar
Keyword(s):  
Banach Space ◽  
Structural Properties ◽  
Orlicz Function ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Orlicz Sequence Spaces ◽  
Vector Valued

AbstractIn this paper we introduce generalized or vector-valued Orlicz-Lorentz sequence spaces l p,q,M(X) on Banach space X with the help of an Orlicz function M and for different positive indices p and q. We study their structural properties and investigate cross and topological duals of these spaces. Moreover these spaces are generalizations of vector-valued Orlicz sequence spaces l M(X) for p = q and also Lorentz sequence spaces for M(x) = x q for q ≥ 1. Lastly we prove that the operator ideals defined with the help of scalar valued sequence spaces l p,q,M and additive s-numbers are quasi-Banach operator ideals for p < q and Banach operator ideals for p ≥ q. The results of this paper are more general than the work of earlier mathematicians, say A. Pietsch, M. Kato, L. R. Acharya, etc.

scholarly journals Norm closed operator ideals in Lorentz sequence spaces

2012 ◽  
Vol 389 (1) ◽  
pp. 247-260 ◽  
Author(s):  
Anna Kamińska ◽  
Alexey I. Popov ◽  
Eugeniu Spinu ◽  
Adi Tcaciuc ◽  
Vladimir G. Troitsky
Keyword(s):  
Closed Operator ◽  
Sequence Spaces ◽  
Operator Ideals

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

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.

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