Zobrazeno 1 - 10
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pro vyhledávání: '"Crouzeix, Michel"'
Autor:
Crouzeix, Michel, Kressner, Daniel
A result by Crouzeix and Palencia states that the spectral norm of a matrix function $f(A)$ is bounded by $K = 1+\sqrt{2}$ times the maximum of $f$ on $W(A)$, the numerical range of $A$. The purpose of this work is to point out that this result exten
Externí odkaz:
http://arxiv.org/abs/2007.09784
Publikováno v:
Bull. London Math. Soc. 50(2018), 986--996
We study different operator radii of homomorphisms from an operator algebra into $B(H)$ and show that these can be computed explicitly in terms of the usual norm. As an application, we show that if $\Omega$ is a $K$-spectral set for a Hilbert space o
Externí odkaz:
http://arxiv.org/abs/1804.04062
Autor:
Crouzeix, Michel, Greenbaum, Anne
We extend the proof in [M.~Crouzeix and C.~Palencia, {\em The numerical range is a $(1 + \sqrt{2})$-spectral set}, SIAM Jour.~Matrix Anal.~Appl., 38 (2017), pp.~649-655] to show that other regions in the complex plane are $K$-spectral sets. In partic
Externí odkaz:
http://arxiv.org/abs/1803.10904
Autor:
Crouzeix, Michel, Palencia, César
It is shown that the numerical range of a linear operator operator in a Hilbert space is a (complete) $(1{+}\sqrt2)$-spectral set. The proof relies, among other things, in the behavior of the Cauchy transform of the conjugates of holomorphic function
Externí odkaz:
http://arxiv.org/abs/1702.00668
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Autor:
Crouzeix, Michel
In an attempt to progress towards proving the conjecture the numerical range W (A) is a 2--spectral set for the matrix A, we propose a study of various constants. We review some partial results, many problems are still open. We describe our correspon
Externí odkaz:
http://arxiv.org/abs/1601.06159
The inf-sup constant for the divergence, or LBB constant, is related to the Cosserat spectrum. It has been known for a long time that on non-smooth domains the Cosserat operator has a non-trivial essential spectrum, which can be used to bound the LBB
Externí odkaz:
http://arxiv.org/abs/1402.3659
Autor:
Beckermann, Bernhard, Crouzeix, Michel
It has been recently shown that $|| F_n(A) ||\leq 2$, where $A$ is a linear continuous operator acting in a Hilbert space, and $F_n$ is the Faber polynomial of degree $n$ corresponding to some convex compact $E\subset \mathbb C$ containing the numeri
Externí odkaz:
http://arxiv.org/abs/1310.1356
Autor:
Crouzeix, Michel, Combescot, Monique
This Letter provides the solution to a yet unsolved basic problem of Solid State Physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50 year old math problem
Externí odkaz:
http://arxiv.org/abs/1111.5801
Autor:
Badea, Catalin, Crouzeix, Michel
Publikováno v:
Oper. Matrices 7 (2013), no. 2, 285--292
Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that the numerical radius of A and of its inverse are no greater than 1+e for some non-negative e. It is shown that the dista
Externí odkaz:
http://arxiv.org/abs/1110.5036