Symmetric and Antisymmetric Tensor Products for the Function-Theoretic Operator Theorist

TL;DR

This paper investigates symmetric and antisymmetric tensor products of Hilbert-space operators, analyzing their norms and spectra, and raises open questions relevant to function-theoretic operator theory.

Contribution

It introduces new analyses of tensor products' norms and spectra, and presents open questions to advance the understanding in function-theoretic operator theory.

Findings

Analysis of norms and spectra for tensor products

Identification of open questions in the field

Focus on well-known classes of operators

Abstract

We study symmetric and antisymmetric tensor products of Hilbert-space operators, focusing on norms and spectra for some well-known classes favored by function-theoretic operator theorists. We pose many open questions that should interest the field.