The Spectral Radius Formula for Fourier–Stieltjes Algebras

A formula for the inner spectral radius

Spectral Radius Algebras and Shift

We consider spectral radius algebras associated to operators of the form h(S), where h ∈ H∞ and S is the unilateral shift. We show that, for a large class of H∞ functions, Bh(S) is weakly dense in LH. In this paper we continue the study of the spectral radius algebras (SRA) initiated in [2]. These algebras represent a very interesting class of non-selfadjoint, non-closed operator algebras. Furt...

The spectral radius in partially ordered algebras

We prove theorems of Perron–Frobenius type for positive elements in partially ordered topological algebras satisfying certain hypotheses. We show how some of our results relate to known results on Banach algebras. We give examples and state some open questions. © 2005 Elsevier Inc. All rights reserved. AMS classification: 47A10; 46H35; 47B65; 15A48

The Sign-Real Spectral Radius for Real Tensors

In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.

Spectral Radius Algebras and C0 Contractions

We consider spectral radius algebras associated to C0 contractions. When the operator A is algebraic, we describe all invariant subspaces that are common for operators in its spectral radius algebra BA. In all other situations BA is weakly dense and we characterize a set of rank one operators in BA that is weakly dense in L(H).