Annals of Functional Analysis

Products of Laurent operators and fields of values

Natália Bebiano and João da Providência

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One of the most fundamental properties of the field of values of an operator is the inclusion of the spectrum within its closure. Obtaining information on the spectrum of products of operators in terms of this spectral inclusion region is a demanding issue. Stating general results seems difficult; however, conclusions can be derived in some special instances. In this paper, we show that the field of values of products of Laurent operators is easily related to the product of their fields of values, and the same occurs for certain classes of Laurent operators with matrix symbols. The results also apply to the class of infinite upper (lower) triangular Toeplitz matrices.

Article information

Ann. Funct. Anal., Volume 7, Number 4 (2016), 552-563.

Received: 4 March 2016
Accepted: 20 March 2016
First available in Project Euclid: 31 August 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46C20: Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.) [See also 47B50]
Secondary: 47A12: Numerical range, numerical radius 47A10: Spectrum, resolvent 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

fields of values spectrum Toeplitz operator Laurent operator symbol


Bebiano, Natália; da Providência, João. Products of Laurent operators and fields of values. Ann. Funct. Anal. 7 (2016), no. 4, 552--563. doi:10.1215/20088752-3661368.

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