New direct proofs of variational principles for t-entropy, spectral radius of weighted shift operators, and entropy statistic theorem

TL;DR

This paper provides new direct proofs for variational principles related to t-entropy, spectral radius of weighted shift operators, and the entropy statistic theorem, establishing their equivalence.

Contribution

It introduces novel direct proofs for key variational principles and demonstrates their equivalence, advancing theoretical understanding in operator entropy.

Findings

Established equivalence of variational principles

Provided new direct proofs for t-entropy and spectral radius

Enhanced theoretical framework for entropy-related operators

Abstract

New direct proofs of variational principles for $t$-entropy, spectral radius of weighted shift operators, and entropy statistic theorem are given. The equivalence of these statements is obtained.