Browsing by Subject "Operator algebras"

Now showing 1 - 3 of 3
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    D-bar and Dirac Type Operators on Classical and Quantum Domains
    (2012-08-29) McBride, Matthew Scott; Klimek, Slawomir; Cowen, Carl C.; Ji, Ron; Dadarlat, Marius
    I study d-bar and Dirac operators on classical and quantum domains subject to the APS boundary conditions, APS like boundary conditions, and other types of global boundary conditions. Moreover, the inverse or inverse modulo compact operators to these operators are computed. These inverses/parametrices are also shown to be bounded and are also shown to be compact, if possible. Also the index of some of the d-bar operators are computed when it doesn't have trivial index. Finally a certain type of limit statement can be said between the classical and quantum d-bar operators on specialized complex domains.
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    Noncommutative geometry of the quantum disk
    (Springer, 2022) Klimek, Slawomir; McBride, Matt; Peoples, J. Wilson; Mathematical Sciences, School of Science
    We discuss various aspects of the noncommutative geometry of a smooth subalgebra of the Toeplitz algebra. In particular, we study the structure of derivations on this subalgebra.
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    Restrictions to Invariant Subspaces of Composition Operators on the Hardy Space of the Disk
    (2014-01-29) Thompson, Derek Allen; Cowen, Carl C.; Ji, Ronghui ; Klimek, Slawomir; Bell, Steven R.; Mukhin, Evgeny
    Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as certain restrictions of the unilateral shift on the Hardy space of the disk. A composition operator with symbol fixing 0 has a nested sequence of invariant subspaces, and if the symbol is linear fractional and extremally noncompact, the restrictions to these subspaces all have the same norm and spectrum. Despite this evidence, we will use semigroup techniques to show many cases where the restrictions are still not unitarily equivalent.