The holomorphic functional calculus approach to operator semigroups

2013 ◽  
Vol 79 (1-2) ◽  
pp. 289-323
Author(s):  
Charles Batty ◽  
Markus Haase ◽  
Junaid Mubeen
Keyword(s):  
Functional Calculus ◽  
Operator Semigroups ◽  
Holomorphic Functional Calculus

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

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 A Besov algebra calculus for generators of operator semigroups and related norm-estimates

2019 ◽  
Author(s):  
Charles Batty ◽  
Alexander Gomilko ◽  
Yuri Tomilov
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Functional Calculus ◽  
The Other ◽  
Direct Approach ◽  
Operator Semigroups ◽  
Holomorphic Semigroups ◽  
Norm Estimates ◽  
Strict Extension ◽  
Bounded Holomorphic

Abstract We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical Hille–Phillips functional calculus, and it is compatible with the other well-known functional calculi. It satisfies the standard properties of functional calculi, provides a unified and direct approach to a number of norm-estimates in the literature, and allows improvements of some of them.

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