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Normal Spectrum of a Subnormal Operator

Electronic Theses of Indian Institute of Science

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Title Normal Spectrum of a Subnormal Operator
 
Creator Kumar, Sumit
 
Subject Hilbert Spaces
Subnormal Operators
Linear Operators
Operator Theory
Subnormal Operators - Normal Spectrum
Minimal Normal Extension(Subnormal Operators)
Quasinormal Operator
Subnormality
Inequalities
C*-algebra
Mathematics
 
Description Let H be a separable Hilbert space over the complex field. The class

S := {N|M : N is normal on H and M is an invariant subspace for Ng of subnormal operators. This notion was introduced by Halmos. The minimal normal extension Ň of a subnormal operator S was introduced by
σ (S) and then Bram proved that
Halmos. Halmos proved that σ(Ň)
(S) is obtained by filling certain number of holes in the spectrum (Ň) of the minimal normal extension Ň of a subnormal operator S.
Let σ (S) := σ (Ň) be the spectrum of the minimal normal extension Ň of S; which is called the normal spectrum of a subnormal operator S: This notion is due to Abrahamse and Douglas. We give several well-known characterization of subnormality. Let C* (S1) and C* (S2) be the C*- algebras generated by S1 and S2 respectively, where S1 and S2 are bounded operators on H:
Next we give a characterization for subnormality which is purely C - algebraic. We also establish an intrinsic characterization of the normal spectrum for a subnormal operator, which enables us to answer the fol-lowing two questions.
Let II be a *- representation from C* (S1) onto C* (S2) such that II(S1) = S2.
If S1 is subnormal, then does it follow that S2 is subnormal? What is the relation between σ (S1) and σ (S2)?
The first question was asked by Bram and second was asked by Abrahamse and Douglas. Answers to these questions were given by Bunce and Deddens.
 
Contributor Misra, Gadadhar
 
Date 2018-03-21T06:42:04Z
2018-03-21T06:42:04Z
2018-03-21
2013
 
Type Thesis
 
Identifier http://hdl.handle.net/2005/3289
http://etd.ncsi.iisc.ernet.in/abstracts/4151/G25645-Abs.pdf
 
Language en_US
 
Relation G25645