The Essential Spectrum of the Essentially Isometric Operator

作者：Mustafayev H S^*

来源：Canadian Mathematical Bulletin, 2014, 57(1): 145-158.

DOI：10.4153/CMB-2012-016-1

• Hilbert space
• contraction
• essentially isometric operator
• (essential) spectrum
• functional calculus

Let T be a contraction on a complex, separable, infinite dimensional Hilbert space and let sigma(T) (resp. sigma(e)(T)) be its spectrum (resp. essential spectrum). We assume that T is an essentially isometric operator; that is, I-H - T* T is compact. We show that if D\sigma T(T) not equal phi, then for every f from the disc-algebra
sigma(e)( f(T)) = f( sigma(e)(T)),
where D is the open unit disc. In addition, if T lies in the class C-0. boolean OR C-.0, then
sigma(e)( f(T)) = f( sigma(T) boolean AND Gamma),
where Gamma is the unit circle. Some related problems are also discussed.

• 出版日期2014-3