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 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 Supersets for the spectrum of elements in extended Banach algebras

1989 ◽  
Vol 12 (4) ◽  
pp. 823-824
Author(s):  
Morteza Seddighin
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Complex Numbers ◽  
Direct Sum

If A is a Banach Algebra with or without an identity, A can be always extended to a Banach algebraA¯with identity, whereA¯is simply the direct sum of A and C, the algebra of complex numbers. In this note we find supersets for the spectrum of elements ofA¯.

Banach algebra with generalized derivations

2017 ◽  
Vol 10 (04) ◽  
pp. 1750069 ◽  
Author(s):  
S. K. Tiwari ◽  
B. Prajapati ◽  
R. K. Sharma
Keyword(s):  
Banach Algebra ◽  
Generalized Derivation ◽  
Complex Numbers ◽  
Complex Field ◽  
Continuous Linear ◽  
Generalized Derivations ◽  
Derivation Formula

Let [Formula: see text] be a unital prime Banach algebra over complex field [Formula: see text] with unity and [Formula: see text] be a nonzero continuous linear generalized derivation associated with a nonzero continuous linear derivation [Formula: see text]. In this paper, we investigate the commutativity of [Formula: see text]. In particular, we prove that a unital prime Banach algebra [Formula: see text] is commutative if one of the following holds; (i) either [Formula: see text] or [Formula: see text], (ii) either [Formula: see text] or [Formula: see text], for sufficiently many [Formula: see text], for any complex numbers [Formula: see text] and an integer [Formula: see text].

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.

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