Results 11 to 20 of about 441 (58)
The Cayley transform of Banach algebras
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 7, Page 427-428, 2002., 2002 The main result of Haynes (1991) is that a square matrix is convergent (limn→∞Dn = 0) if and only if it is the Cayley transform CA = (I−A)−1(I + A) of a stable matrix A. In this note, we show, with a simple proof, that the above is true in a much more general setting of complex Banach algebras.
Zhidong Pan
wiley +1 more source
Continuity and general perturbation of the Drazin inverse for closed linear operators
Abstract and Applied Analysis, Volume 7, Issue 6, Page 335-347, 2002., 2002 We study perturbations and continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and the gap between ranges and nullspaces of operators. The results are used to derive a theorem on the continuity of the Drazin inverse for closed operators and to describe the ...
N. Castro González +2 more
wiley +1 more source
On the weakly closed algebra generated by a unitary operator in a Pontryagin space
, 2018 This work is devoted to a study of a weakly closed algebra generated by polynomials of a unitary operator in a Pontryagin space. In particular, the inverse operator can belong or not to this algebra. The corresponding criteria is obtained.
V. Strauss
semanticscholar +1 more source
Regularized functional calculi, semigroups, and cosine functions for pseudodifferential operators
Abstract and Applied Analysis, Volume 2, Issue 1-2, Page 121-136, 1997., 1997 Let iAj(1 ≤ j ≤ n) be generators of commuting bounded strongly continuous groups, A ≡ (A1, A2, …, An). We show that, when f has sufficiently many polynomially bounded derivatives, then there exist k, r > 0 such that f(A) has a ‐regularized BCk(f(Rn)) functional calculus.
Ralph Delaubenfels, Yansong Lei
wiley +1 more source
On the consequences of a Mihlin-H\"ormander functional calculus: maximal and square function estimates [PDF]
, 2015 We prove that the existence of a Mihlin-H\"ormander functional calculus for an operator $L$ implies the boundedness on $L^p$ of both the maximal operators and the continuous square functions build on spectral multipliers of $L.$ The considered multiplier
Wróbel, Błażej
core +2 more sources
On cross-correlation of a hyperfunction and a real analytic function
, 2015 We describe the cross-correlation operator over the space of realanalytic functions and generalize classic Schwartz’s theorem on shiftinvariant operators.
M. Patra, S. Sharyn
semanticscholar +1 more source
Chebyshev type inequalities for Hilbert space operators [PDF]
, 2014 We establish several operator extensions of the Chebyshev inequality. The main version deals with the Hadamard product of Hilbert space operators.
Mohammad Sal +2 more
core +1 more source
An Operator Extension of Čebyšev Inequality
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 Some operator inequalities for synchronous functions that are related to the čebyšev inequality are given. Among other inequalities for synchronous functions it is shown that ∥ø(f(A)g(A)) - ø(f(A))ø(g(A))∥ ≤ max{║ø(f2(A)) - ø2(f(A))║, ║ø)G2(A)) - ø2(g(A))
Moradi Hamid Reza +2 more
doaj +1 more source
Spectral multipliers for Laplacians with drift on Damek-Ricci spaces [PDF]
, 2013 We prove a multiplier theorem for certain Laplacians with drift on Damek-Ricci spaces, which are a class of Lie groups of exponential growth. Our theorem generalizes previous results obtained by W. Hebisch, G. Mauceri and S.
Ottazzi, Alessandro, Vallarino, Maria
core +1 more source
How to compare the absolute values of operator sums and the sums of absolute values
, 2012 We address the problem of comparing |A+B| and |A|+ |B| , for A,B ∈Mn(C) . Some results are obtained by using a technique of positive linear maps and several open questions are proposed.
Eun-young Lee
semanticscholar +1 more source