Operator algebras generated by left invertibles
Abstract
Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*algebras. The primary object of this paper is the normclosed operator algebra generated by a left invertible $T$ together with its MoorePenrose inverse $T^\dagger$. We denote this algebra by $\mathfrak{A}_T$. In the isometric case, $T^\dagger = T^*$ and $\mathfrak{A}_T$ is a representation of the Toeplitz algebra. Of particular interest is the case when $T$ satisfies a nondegeneracy condition called analytic. We show that $T$ is analytic if and only if $T^*$ is CowenDouglas. When $T$ is analytic with Fredholm index $1$, the algebra $\mathfrak{A}_T$ contains the compact operators, and any two such algebras are boundedly isomorphic if and only if they are similar.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.04700
 Bibcode:
 2018arXiv180904700D
 Keywords:

 Mathematics  Operator Algebras;
 47L55;
 47A53;
 47B32;
 47B20