The Essential Spectrum of the Essentially Isometric Operator

2014 ◽  
Vol 57 (1) ◽  
pp. 145-158
Author(s):  
H. S. Mustafayev
Keyword(s):  
Hilbert Space ◽  
Unit Circle ◽  
Essential Spectrum ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Isometric Operator ◽  
Disc Algebra ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space

AbstractLet T be a contraction on a complex, separable, infinite dimensional Hilbert space and let σ(T) (resp. σe(T)) be its spectrum (resp. essential spectrum). We assume that T is an essentially isometric operator; that is, IH -T*T is compact. We show that if D\σ(T) ≠ Ø, then for every f from the disc-algebraσe(f(T)) = f(σe(T))where D is the open unit disc. In addition, if T lies in the class C0.∪ C.0, thenσe(f(T)) = f(σ(T) ∩ Γ),where Γ is the unit circle. Some related problems are also discussed.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
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