Spectral radius algebras, Deddens algebras, and weighted shifts

Inductive Limit Algebras from Periodic Weighted Shifts on Fock Space

Noncommutative multivariable versions of weighted shift operators arise naturally as ‘weighted’ left creation operators acting on the Fock space Hilbert space. We identify a natural notion of periodicity for these N tuples, and then find a family of inductive limit algebras determined by the periodic weighted shifts which can be regarded as noncommutative multivariable generalizations of the Bu...

Linear Maps Preserving Invertibility or Spectral Radius on Some $C^{*}$-algebras

Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.

CONTINUITY IN FUNDAMENTAL LOCALLY MULTIPLICATIVE TOPOLOGICAL ALGEBRAS

Abstract. In this paper, we first derive specific results concerning the continuity and upper semi-continuity of the spectral radius and spectrum functions on fundamental locally multiplicative topological algebras. We continue our investigation by further determining the automatic continuity of linear mappings and homomorphisms in these algebras.

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Deddens Algebras and Shift

The unilateral shift S acting on Hilbert space H is one of the most studied operators. Much is known about its structure, and this success is in large part due to the identification of S with the operator of multiplication by z on H — the Hardy space on the unit disk. From the function theory point of view, the commutant {S}′ is then simply H∞, the Hardy space of essentially bounded functions o...