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

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 Extrapolation properties of closed operator ideals

2013 ◽  
Vol 38 ◽  
pp. 341-350 ◽  
Author(s):  
Luz M. Fernández-Cabrera ◽  
Antón Martínez
Keyword(s):  
Closed Operator ◽  
Operator Ideals

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 Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Awad A. Bakery ◽  
Mustafa M. Mohammed
Keyword(s):  
Orlicz Function ◽  
Sufficient Conditions ◽  
Operator Ideal ◽  
Linear Operators ◽  
Sequence Spaces ◽  
Operator Ideals ◽  
Bounded Linear ◽  
Cesàro Mean ◽  
Inclusion Relations ◽  
Cesaro Mean

In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces cesφ, where φ is an Orlicz function such that the class Scesφ of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers which belong to cesφ forms an operator ideal. The completeness and denseness of its ideal components are specified and Scesφ constructs a pre-quasi Banach operator ideal. Some inclusion relations between the pre-quasi operator ideals and the inclusion relations for their duals are explained. Moreover, we have presented the sufficient conditions on cesφ such that the pre-quasi Banach operator ideal generated by approximation number is small. The above results coincide with that known for cesp  (1<p<∞).

scholarly journals INTERPOLATION METHODS DEFINED BY MEANS OF POLYGONS AND COMPACT OPERATORS

2007 ◽  
Vol 50 (3) ◽  
pp. 653-671 ◽  
Author(s):  
Luz M. Fernández-Cabrera ◽  
Antón Martínez
Keyword(s):  
Banach Spaces ◽  
Necessary Conditions ◽  
Closed Operator ◽  
Compact Operators ◽  
Operator Ideals ◽  
Interpolation Methods

AbstractWe work with interpolation methods for $N$-tuples of Banach spaces associated with polygons. We compare necessary conditions for interpolating closed operator ideals with conditions required to interpolate compactness. We also establish a formula for the measure of non-compactness of interpolated operators.

Closed operator ideals and limiting real interpolation

2014 ◽  
Vol 220 (2) ◽  
pp. 187-196 ◽  
Author(s):  
Luz M. Fernández-Cabrera ◽  
Antón Martínez
Keyword(s):  
Closed Operator ◽  
Real Interpolation ◽  
Operator Ideals
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