University of Illinois Urbana-Champaign

Bishop's Condition Beta and Decomposable Operators

Snader, Jon Christopher

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https://hdl.handle.net/2142/71207

Description

Title
Bishop's Condition Beta and Decomposable Operators
Author(s)
Snader, Jon Christopher
Issue Date
1982
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Abstract
  • This thesis considers the notions of decomposable operators in the sense of C. Foias, and a certain analytic condition--called condition ((beta))--due to Errett Bishop. It is shown that the concepts are related, and that each can be used to study the other. In particular, it is shown how Bishop's condition can be exploited in the study of decomposable operators.
  • The main part of the thesis is divided into three parts. In the first part, condition ((beta)) itself is studied intensively. The stability of condition ((beta)) under restriction, similarity transformations, the adjoint operation, compact perturbations and other changes of operator is explored. Some necessary conditions for an operator to have condition ((beta)) are established, and its relationship to the related notion of the single-valued extension property is studied.
  • In the second part, results from the first are used to study strongly analytic subspaces in the sense of Lange, and to obtain a characterization of strongly decomposable operators on a reflexive Banach space.
  • In the last part, a subclass of the decomposable operators, called the T-strongly decomposable operators, is studied. Results from the first two parts are used to obtain sufficient conditions for an operator to be T-strongly decomposable.
Graduation Semester
1982
Type of Resource
text
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http://hdl.handle.net/2142/71207

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