Preprint Article Version 1 This version is not peer-reviewed

Hypo-q-Norms on a Cartesian Product of Algebras of Operators on Banach Spaces

Version 1 : Received: 19 December 2017 / Approved: 19 December 2017 / Online: 19 December 2017 (10:31:23 CET)

How to cite: Dragomir, S.S. Hypo-q-Norms on a Cartesian Product of Algebras of Operators on Banach Spaces. Preprints 2017, 2017120136 (doi: 10.20944/preprints201712.0136.v1). Dragomir, S.S. Hypo-q-Norms on a Cartesian Product of Algebras of Operators on Banach Spaces. Preprints 2017, 2017120136 (doi: 10.20944/preprints201712.0136.v1).

Abstract

In this paper we introduce the hypo-q-operator norm and hypo-q-numerical radius on a Cartesian product of algebras of bounded linear operators on Banach spaces. A representation of these norms in terms of semi-inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given.

Subject Areas

normed spaces; cartesian products of normed spaces; inequalities; reverse inequalities; shisha-mond type inequalities

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