Spectra of constructs of a system of operators

Angel Carrillo; Carlos Hernández

doi:10.1090/S0002-9939-1984-0744643-5

Spectra of constructs of a system of operators

Angel Carrillo, Carlos Hernández

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6 Scopus citations

Abstract

This paper describes the spectrum and the upper and lower Fredholm spectra of (n + m)-tuples (F(A₁),., F(A_n), G(B₁),., G(B_m)) of operators, where (A_i) and (B_j) are systems of operators in two Hilbert spaces H₁ and H₂, and F and G are certain linear operators defined on L(Hi). Using spectral mapping theorems the spectra of operators constructed by the action of a polynomial on a system (F(A₁),., F(A_n), G(B₁),., G(B_m)) is obtained. In particular, the spectra of the elementary operator and tensor products of operators is determined.

Original language	English
Pages (from-to)	426-432
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	91
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1984-0744643-5
State	Published - Jul 1984
Externally published	Yes

Keywords

Elementary operator
Essential spectrum
Fredholm operator
Joint spectrum
Spectral mapping theorem
Spectrum
Tensor products
Upper and lower Fredholm spectra

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10.1090/S0002-9939-1984-0744643-5

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title = "Spectra of constructs of a system of operators",

abstract = "This paper describes the spectrum and the upper and lower Fredholm spectra of (n + m)-tuples (F(A1),., F(An), G(B1),., G(Bm)) of operators, where (Ai) and (Bj) are systems of operators in two Hilbert spaces H1 and H2, and F and G are certain linear operators defined on L(Hi). Using spectral mapping theorems the spectra of operators constructed by the action of a polynomial on a system (F(A1),., F(An), G(B1),., G(Bm)) is obtained. In particular, the spectra of the elementary operator and tensor products of operators is determined.",

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T1 - Spectra of constructs of a system of operators

AU - Carrillo, Angel

AU - Hernández, Carlos

PY - 1984/7

Y1 - 1984/7

N2 - This paper describes the spectrum and the upper and lower Fredholm spectra of (n + m)-tuples (F(A1),., F(An), G(B1),., G(Bm)) of operators, where (Ai) and (Bj) are systems of operators in two Hilbert spaces H1 and H2, and F and G are certain linear operators defined on L(Hi). Using spectral mapping theorems the spectra of operators constructed by the action of a polynomial on a system (F(A1),., F(An), G(B1),., G(Bm)) is obtained. In particular, the spectra of the elementary operator and tensor products of operators is determined.

AB - This paper describes the spectrum and the upper and lower Fredholm spectra of (n + m)-tuples (F(A1),., F(An), G(B1),., G(Bm)) of operators, where (Ai) and (Bj) are systems of operators in two Hilbert spaces H1 and H2, and F and G are certain linear operators defined on L(Hi). Using spectral mapping theorems the spectra of operators constructed by the action of a polynomial on a system (F(A1),., F(An), G(B1),., G(Bm)) is obtained. In particular, the spectra of the elementary operator and tensor products of operators is determined.

KW - Elementary operator

KW - Essential spectrum

KW - Fredholm operator

KW - Joint spectrum

KW - Spectral mapping theorem

KW - Spectrum

KW - Tensor products

KW - Upper and lower Fredholm spectra

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DO - 10.1090/S0002-9939-1984-0744643-5

M3 - Artículo

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SN - 0002-9939

VL - 91

SP - 426

EP - 432

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 3

ER -

Spectra of constructs of a system of operators

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