Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals

In: Mathematica Slovaca, vol. 64, no. 6

Manjul Gupta - Antara Bhar

Detaily:

Rok, strany: 2014, 1475 - 1496

Kľúčové slová:

Lorentz sequence spaces, s-numbers of operators, Orlicz function and Orlicz sequence spaces, operator ideals

DOI: https://doi.org/10.2478/s12175-014-0287-6

O článku:

In 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

Ako citovať:

ISO 690:

Gupta, M., Bhar, A. 2014. Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals. In Mathematica Slovaca, vol. 64, no.6, pp. 1475-1496. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0287-6

APA:

Gupta, M., Bhar, A. (2014). Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals. Mathematica Slovaca, 64(6), 1475-1496. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0287-6

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