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Spectrum preserving linear mappings in Banach algebras

B. Aupetit, H. du T. Mouton (1994)

Studia Mathematica

Let A and B be two unitary Banach algebras. We study linear mappings from A into B which preserve the polynomially convex hull of the spectrum. In particular, we give conditions under which such surjective linear mappings are Jordan morphisms.

Splines and pseudo-inverses

F. J. Delvos (1978)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Square functions, bounded analytic semigroups, and applications

Christian Le Merdy (2007)

Banach Center Publications

To any bounded analytic semigroup on Hilbert space or on L p -space, one may associate natural ’square functions’. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative L p -spaces, Banach lattices, and their subspaces. We give some applications to H functional calculus, similarity problems, multiplier theory, and control theory.

Squaring a reverse AM-GM inequality

Minghua Lin (2013)

Studia Mathematica

Let A, B be positive operators on a Hilbert space with 0 < m ≤ A, B ≤ M. Then for every unital positive linear map Φ, Φ²((A + B)/2) ≤ K²(h)Φ²(A ♯ B), and Φ²((A+B)/2) ≤ K²(h)(Φ(A) ♯ Φ(B))², where A ♯ B is the geometric mean and K(h) = (h+1)²/(4h) with h = M/m.

Stability of infinite ranges and kernels

K.-H. Förster, V. Müller (2006)

Studia Mathematica

Let A(·) be a regular function defined on a connected metric space G whose values are mutually commuting essentially Kato operators in a Banach space. Then the spaces R ( A ( z ) ) and N ( A ( z ) ) ¯ do not depend on z ∈ G. This generalizes results of B. Aupetit and J. Zemánek.

Stability of the bases and frames reproducing kernels in model spaces

Anton Baranov (2005)

Annales de l'institut Fourier

We study the bases and frames of reproducing kernels in the model subspaces K Θ 2 = H 2 Θ H 2 of the Hardy class H 2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels k λ n ( z ) = ( 1 - Θ ( λ n ) ¯ Θ ( z ) ) / ( z - λ ¯ n ) under “small” perturbations of the points λ n . We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces K Θ 2 and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.

Stability of the index of a linear relation under compact perturbations

Dana Gheorghe (2007)

Studia Mathematica

We prove the stability under compact perturbations of the algebraic index of a Fredholm linear relation with closed range acting between normed spaces. Our main tool is a result concerning the stability of the index of a complex of Banach spaces under compact perturbations.

Currently displaying 221 – 240 of 335