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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Fredholm spectra of £f-Toeplitz operators

Chen, Chih-Hao 25 July 2011 (has links)
Abstract Let £f be a complex number in the closed unit disc , and H be a separable Hilbert space with the orthonormal basis, say,£`= {en : n =0 , 1 , 2¡K}. A bounded operator T on H is called a £f-Toeplitz operator if <Tem+1 , en+1> =£f <Tem , en> (where <¡E,¡E> is the inner product on H).If the function £p can be represented as a linear combination of the above orthonormal basis with the coefficients an=<Te0 ,en >, n≥ 0,and an=<Telnl ,e0 >, n<0, then we call this the symbol of T . The subject arises naturally from a special case of the operator equation S*AS =£fA + B; where S is a shift on H , and in this operator equation the matrix A can solve a special set of simultaneous equations. It is also clear that the well-known Toeplitz operators are precisely the solutions of S*AS = A, when S is the unilateral shift.In this paper,we will review the similarities and differences between £f-Toeplitz operators and Toeplitz operators. The main purpose is to generalize the well-known Coburn's characterization for the essential spectrum(or,the same in this case,spectrum)for Toeplitz operators to £f-Toeplitz operators.

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