scholarly journals On non-holomorphic functional calculus for commuting operators

2003 ◽  
Vol 93 (1) ◽  
pp. 109 ◽  
Author(s):  
Sebastian Sandberg
Keyword(s):  
Cohomology Class ◽  
Functional Calculus ◽  
General Scheme ◽  
Holomorphic Functions ◽  
Holomorphic Functional Calculus ◽  
Resolvent Identity ◽  
Commuting Operators

We provide a general scheme to extend Taylor's holomorphic functional calculus for several commuting operators to classes of non-holomorphic functions. These classes of functions will depend on the growth of the operator valued forms that define the resolvent cohomology class. The proofs are based on a generalization of the so-called resolvent identity to several 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 Holomorphic functional calculi and sums of commuting opertors

1998 ◽  
Vol 58 (2) ◽  
pp. 291-305 ◽  
Author(s):  
David Albrecht ◽  
Edwin Franks ◽  
Alan McIntosh
Keyword(s):  
Banach Space ◽  
Holomorphic Function ◽  
Functional Calculus ◽  
Holomorphic Functional Calculus ◽  
Regularity Problem ◽  
Commuting Operators ◽  
Consistent Manner ◽  
Holomorphic Functional Calculi ◽  
The Individual

Let S and T be commuting operators of type ω and type ϖ in a Banach space X. Then the pair has a joint holomorphic functional calculus in the sense that it is possible to define operators f(S, T) in a consistent manner, when f is a suitable holomorphic function defined on a product of sectors. In particular, this gives a way to define the sum S + T when ω + ϖ < π. We show that this operator is always of type μ where μ = max{ω, ϖ}. We explore when bounds on the individual functional calculi of S and T imply bounds on the functional calculus of the pair (S, T), and some implications for the regularity problem of when ∥(S + T)u∥ is equivalent to ∥Su∥ + ∥Tu∥.

scholarly journals Bicomplex holomorphic functional calculus

2013 ◽  
Vol 287 (10) ◽  
pp. 1093-1105 ◽  
Author(s):  
Fabrizio Colombo ◽  
Irene Sabadini ◽  
Daniele C. Struppa
Keyword(s):  
Functional Calculus ◽  
Holomorphic Functional Calculus

scholarly journals A SHORT PROOF THAT Mn(A) IS LOCAL IF A IS LOCAL AND FRÉCHET

1992 ◽  
Vol 03 (04) ◽  
pp. 581-589 ◽  
Author(s):  
LARRY B. SCHWEITZER
Keyword(s):  
Banach Algebra ◽  
Functional Calculus ◽  
Short Proof ◽  
Complex Numbers ◽  
Holomorphic Functional Calculus ◽  
General Proof

We give a short and very general proof of the fact that the property of a dense Fréchet subalgebra of a Banach algebra being local, or closed under the holomorphic functional calculus m the Banach algebra, is preserved by tensoring with the n×n matnx algebra of the complex numbers

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