منابع مشابه
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...
متن کاملWeak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups
Let S be a locally compact foundation semigroup with identity and be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of In this paper, we prove that X is invariantly complemented in if and only if the left ideal of has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...
متن کاملSpectral radius algebras, Deddens algebras, and weighted shifts
We determine the extended eigenvalues and extended eigenvectors of weighted shifts. We also describe the structure of Deddens algebras and spectral radius algebras associated to weighted shifts. In particular, we show that these algebras are weakly dense in the algebra of all bounded linear operators or in the algebra of lower triangular operators.
متن کاملInvariant Subspaces and Hyper-reflexivity for Free Semigroup Algebras
In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very str...
متن کاملLie-algebras and Linear Operators with Invariant Subspaces
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with the above property must have a representation as a polynomial element of the universal enveloping algebra of some algebra of differential (difference) opera...
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ژورنال
عنوان ژورنال: Expositiones Mathematicae
سال: 2015
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2014.04.004