Corpus ID: 119157447

Operator Algebras Generated by Left Invertibles

@article{DeSantis2019OperatorAG,
  title={Operator Algebras Generated by Left Invertibles},
  author={Derek DeSantis},
  journal={arXiv: Operator Algebras},
  year={2019}
}
  • Derek DeSantis
  • Published 12 September 2018
  • Mathematics
  • arXiv: Operator Algebras
Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*-algebras. Motivated by questions from linear equations in Hilbert spaces (frame theory), we instigate a research program on concrete operator algebras that arise from directed graphs. In this paper, we consider the norm-closed operator algebra $\mathfrak{A}_T$ generated by a left invertible $T$ together with its Moore-Penrose inverse $T^\dagger$. In the isometric… Expand

References

SHOWING 1-10 OF 49 REFERENCES
Norming algebras and automatic complete boundedness of isomorphisms of operator algebras
We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A 1 and A 2 are operator algebras, then any bounded epimorphism of A 1 onto A 2Expand
Algebras generated by a subnormal operator
We use the notion of generalized Toeplitz operators to obtain some basic results concerning the C*-algebra generated by a subnormal operator. We apply these results to problems concerning theExpand
A Characterization of Operator Algebras
Abstract An operator algebra is a uniformly closed algebra of bounded operators on a Hilbert space. In this paper we give a characterization of unital operator algebras in terms of their matricialExpand
FRAMES IN HILBERT C*-MODULES AND C*-ALGEBRAS
We present a general approach to a module frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the ideas of geometric dilation to standard Hilbert C*-modules over unitalExpand
K-GROUPS OF BANACH ALGEBRAS AND STRONGLY IRREDUCIBLE DECOMPOSITIONS OF OPERATORS
A bounded linear operator T on the Hilbert space H is called strongly irreducible if T does not commute with any nontrivial idempotent operator. One says that T has a finite (SI) decomposition if TExpand
Similarity Classification of Cowen-Douglas Operators
Abstract Let $\mathcal{H}$ be a complex separable Hilbert space and $\mathcal{L}\left( \mathcal{H} \right)$ denote the collection of bounded linear operators on $\mathcal{H}$ . An operator $A$ inExpand
Invariant subspaces in Banach spaces of analytic functions
We study the invariant subspace structure of the operator of multiplication by z, Mz, on a class of Banach spaces of analytic functions. For operators on Hilbert spaces our class coincides with theExpand
PURE SUBNORMAL OPERATORS HAVE CYCLIC ADJOINTS
Abstract We shall prove that a pure subnormal operator has a cyclic adjoint. This answers a question raised by J. Deddens and W. Wogen in 1976. We first prove that a subnormal operatorSon a HilbertExpand
K-group and similarity classification of operators
Abstract Let H be a complex separable Hilbert space and L ( H ) denote the collection of bounded linear operators on H . An operator A in L ( H ) is said to be a Cowen–Douglas operator if there existExpand
Structure and classification of C.-algebras
We give an overview of the development over the last 15 years of the theory of simple C.-algebras, in particular in regards to their classification and structure. We discuss dimension theory forExpand
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