SEQUENCE SPACES OF OPERATORS ON l<sub>2</sub>

Let [Formula: see text] be fixed. For each [Formula: see text], we define the set [Formula: see text] of sequences of infinite complex matrices and the norm [Formula: see text] on [Formula: see text] analogously to the classical sequence space [Formula: see text] and the [Formula: see text]-norm as follows: [Formula: see text] and [Formula: see text] where [Formula: see text] is referred to as the operator norm on [Formula: see text]. We first study the completeness of sequence space [Formula: see text] equipped with the norm [Formula: see text]. Some duality results are also discussed. The aim of this paper is to show that for the case where [Formula: see text], the dual [Formula: see text] of [Formula: see text] can be decomposed as an [Formula: see text] direct-sum of its two closed subspaces. This is done by a way analogous to the theorem of Dixmier on decomposing the dual [Formula: see text] of [Formula: see text].

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SEQUENCE SPACES OF OPERATORS ON l₂

Abstract: Abstract. In this paper, we define some new sequence spaces of infinite matrices regarded as operators on l 2 by using algebraic properties of such the matrices under the Schur product multiplication. Some of their basic properties as well as duality and preduality are discussed.

Cited by 2 publications

References 6 publications

Spectrum localizations for matrix operators on lp spaces

Spectrum localizations for matrix operators on lp spaces

Duality decompositions of some matrix sequence spaces

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SEQUENCE SPACES OF OPERATORS ON l2

Abstract: Abstract. In this paper, we define some new sequence spaces of infinite matrices regarded as operators on l 2 by using algebraic properties of such the matrices under the Schur product multiplication. Some of their basic properties as well as duality and preduality are discussed.

Cited by 2 publications

References 6 publications

Spectrum localizations for matrix operators on lp spaces

Spectrum localizations for matrix operators on lp spaces

Duality decompositions of some matrix sequence spaces

Contact Info

Product

Resources

About

SEQUENCE SPACES OF OPERATORS ON l₂