scholarly journals The analytic-functional calculus for several commuting operators

1970 ◽  
Vol 125 (0) ◽  
pp. 1-38 ◽  
Author(s):  
Joseph L. Taylor
Keyword(s):  
Functional Calculus ◽  
Analytic Functional ◽  
Commuting Operators

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.

Local properties of Taylor's analytic functional calculus

1982 ◽  
Vol 68 (1) ◽  
pp. 103-116 ◽  
Author(s):  
J�rg Eschmeier
Keyword(s):  
Functional Calculus ◽  
Analytic Functional ◽  
Local Properties

scholarly journals Discrete quadratic estimates and holomorphic functional calculi in Banach spaces

1998 ◽  
Vol 58 (2) ◽  
pp. 271-290 ◽  
Author(s):  
Edwin Franks ◽  
Alan McIntosh
Keyword(s):  
Functional Calculus ◽  
Sufficient Conditions ◽  
Uniform Norm ◽  
Commuting Operators ◽  
Orthonormal Sequence ◽  
Quadratic Estimates ◽  
Holomorphic Functional Calculi ◽  
Necessary And Sufficient ◽  
Dyadic Decomposition ◽  
Uniformly Bounded

We develop a discrete version of the weak quadratic estimates for operators of type w explained by Cowling, Doust, McIntosh and Yagi, and show that analogous theorems hold. The method is direct and can be generalised to the case of finding necessary and sufficient conditions for an operator T to have a bounded functional calculus on a domain which touches σ(T) nontangentially at several points. For operators on Lp, 1 < p < ∞, it follows that T has a bounded functional calculus if and only if T satisfies discrete quadratic estimates. Using this, one easily obtains Albrecht's extension to a joint functional calculus for several commuting operators. In Hilbert space the methods show that an operator with a bounded functional calculus has a uniformly bounded matricial functional calculus.The basic idea is to take a dyadic decomposition of the boundary of a sector Sv. Then on the kth ingerval consider an orthonormal sequence of polynomials . For h ∈ H∞(Sν), estimates for the uniform norm of h on a smaller sector Sμ are obtained from the coefficients akj = (h, ek, j). These estimates are then used to prove the theorems.

scholarly journals Analytic functional calculus

1985 ◽  
Vol 55 (2) ◽  
pp. 209
Author(s):  
Gian-Carlo Rota
Keyword(s):  
Functional Calculus ◽  
Analytic Functional
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