Joint Spectrum of Commuting Operators with Compact Imaginary Parts

1995 ◽  
pp. 81-91
Author(s):  
M. S. Livšic ◽  
N. Kravitsky ◽  
A. S. Markus ◽  
V. Vinnikov
Keyword(s):  
Joint Spectrum ◽  
Commuting Operators

scholarly journals Simultaneous Upper Triangular Forms for Commuting Operators in a Finite von Neumann Algebra

2019 ◽  
Vol 72 (5) ◽  
pp. 1188-1245
Author(s):  
Ian Charlesworth ◽  
Ken Dykema ◽  
Fedor Sukochev ◽  
Dmitriy Zanin
Keyword(s):  
Functional Calculus ◽  
Von Neumann Algebra ◽  
Von Neumann ◽  
Holomorphic Functional Calculus ◽  
Joint Spectrum ◽  
Natural Properties ◽  
Tracial State ◽  
Commuting Operators ◽  
Finite Von Neumann Algebra

AbstractThe joint Brown measure and joint Haagerup–Schultz projections for tuples of commuting operators in a von Neumann algebra equipped with a faithful tracial state are investigated, and several natural properties are proved for these. It is shown that the support of the joint Brown measure is contained in the Taylor joint spectrum of the tuple, and also in the ostensibly smaller left Harte spectrum. A simultaneous upper triangularization result for finite commuting tuples is proved, and the joint Brown measure and joint Haagerup–Schultz projections are shown to behave well under the Arens multivariate holomorphic functional calculus of such a commuting tuple.

scholarly journals Joint spectra and joint numerical ranges for pairwise commuting operators in Banach spaces

1988 ◽  
Vol 30 (2) ◽  
pp. 145-153 ◽  
Author(s):  
Volker Wrobel
Keyword(s):  
Banach Space ◽  
Convex Hull ◽  
Banach Algebra ◽  
Banach Spaces ◽  
Numerical Range ◽  
Linear Operators ◽  
Continuous Linear ◽  
Joint Spectrum ◽  
Commuting Operators ◽  
Continuous Linear Operators

In a recent paper M. Cho [5] asked whether Taylor's joint spectrum σ(a1, …, an; X) of a commuting n-tuple (a1,…, an) of continuous linear operators in a Banach space X is contained in the closure V(a1, …, an; X)- of the joint spatial numerical range of (a1, …, an). Among other things we prove that even the convex hull of the classical joint spectrum Sp(a1, …, an; 〈a1, …, an〉), considered in the Banach algebra 〈a1, …, an〉, generated by a1, …, an, is contained in V(a1, …, an; X)-.

scholarly journals Joint spectra for commuting operators

1985 ◽  
Vol 28 (2) ◽  
pp. 233-248 ◽  
Author(s):  
A. KällstrÖm ◽  
B.D. Sleeman
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Chain Complex ◽  
Joint Spectrum ◽  
Commuting Operators ◽  
A Chain

The theory of joint spectra for commuting operators in a Hilbert space has recently been studied by several authors (Vasilescu [11,12], Curto [4,5], and Cho-Takaguchi[2,3]). In this paper we willuse the definition by Taylor [10] of the joint spectrum to show that thejoint spectrum is determined by the action of certain "Laplacians"(cf. Curto [4,5]) of a chain-complex of Hilbert spaces.

scholarly journals A joint spectrum for several commuting operators

1970 ◽  
Vol 6 (2) ◽  
pp. 172-191 ◽  
Author(s):  
Joseph L Taylor
Keyword(s):  
Joint Spectrum ◽  
Commuting Operators

Multiparameter problems and joint spectra

1982 ◽  
Vol 93 (1-2) ◽  
pp. 129-135 ◽  
Author(s):  
D. F. McGhee
Keyword(s):  
Bounded Operators ◽  
Joint Spectrum ◽  
Intimate Connection ◽  
Commuting Operators ◽  
Multiparameter Problem ◽  
Adjoint Operators

SynopsisIn this paper, we demonstrate an intimate connection between the spectrum of a multiparameter problem and the joint spectrum of an associated set of commuting operators, and show that the spectrum of a multiparameter problem involving bounded operators is non-empty. Multiparameter systems involving compact and self-adjoint operators are considered, and some simplification of results in the literature are noted.

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