Preprint Article Version 1 This version is not peer-reviewed

Hypo-q-Norms on Cartesian Products of Algebras of Bounded Linear Operators on Hilbert Spaces

Version 1 : Received: 4 December 2017 / Approved: 4 December 2017 / Online: 4 December 2017 (05:43:58 CET)

How to cite: Dragomir, S.S. Hypo-q-Norms on Cartesian Products of Algebras of Bounded Linear Operators on Hilbert Spaces. Preprints 2017, 2017120016 (doi: 10.20944/preprints201712.0016.v1). Dragomir, S.S. Hypo-q-Norms on Cartesian Products of Algebras of Bounded Linear Operators on Hilbert Spaces. Preprints 2017, 2017120016 (doi: 10.20944/preprints201712.0016.v1).

Abstract

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of 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. Several bounds for the norms δp, ϑp and the real norms ηr,p and θr,p are provided as well.

Subject Areas

Hilbert spaces; bounded linear operators; operator norm and numerical radius; n-tuple of operators; operator inequalities

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