Majoration des semi-groupes de contractions de L1 et applications
Majoration du nombre de résonances près de l'axe réel (d'après un travail avec M. Zworski)
Mappings into spaces of operators
Maps on matrices that preserve the spectral radius distance
Let ϕ be a surjective map on the space of n×n complex matrices such that r(ϕ(A)-ϕ(B))=r(A-B) for all A,B, where r(X) is the spectral radius of X. We show that ϕ must be a composition of five types of maps: translation, multiplication by a scalar of modulus one, complex conjugation, taking transpose and (simultaneous) similarity. In particular, ϕ is real linear up to a translation.
Maps preserving numerical radius distance on C*-algebras
We characterize surjective nonlinear maps Φ between unital C*-algebras 𝒜 and ℬ that satisfy w(Φ(A)-Φ(B))) = w(A-B) for all A,B ∈ 𝒜 under a mild condition that Φ(I) - Φ(0) belongs to the center of ℬ, where w(A) is the numerical radius of A and I is the unit of 𝒜.
Marcinkiewicz multipliers of higher variation and summability of operator-valued Fourier series
Let , where, for 1 ≤ r < ∞, (resp., ) denotes the class of functions (resp., bounded functions) g: → ℂ such that g has bounded r-variation (resp., uniformly bounded r-variations) on (resp., on the dyadic arcs of ). In the author’s recent article [New York J. Math. 17 (2011)] it was shown that if is a super-reflexive space, and E(·): ℝ → () is the spectral decomposition of a trigonometrically well-bounded operator U ∈ (), then over a suitable non-void open interval of r-values, the condition...
Markov operators: applications to diffusion processes and population dynamics
This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.
Mathematical analysis of electromagnetic open Waveguides
Matrix and operator inequalities.
Matrix order in Bohr inequality for operators.
Matrix trace inequalities on the Tsallis entropies.
Maximal invariant neutral subspaces and an application to the algebraic Riccati equation.
Maximal Monotonicity of Operators with Sufficiently Large Domain and Application to the Hartree Problem.
Mazur-Orlicz equality
A remarkable theorem of Mazur and Orlicz which generalizes the Hahn-Banach theorem is here put in a convenient form through an equality which will be referred to as the Mazur-Orlicz equality. Applications of the Mazur-Orlicz equality to lower barycenters for means, separation principles, Lax-Milgram lemma in reflexive Banach spaces, and monotone variational inequalities are provided.
MD-numbers and asymptotic MD-numbers of operators.
Mean ergodicity for compact operators
A mean ergodic theorem is proved for a compact operator on a Banach space without assuming mean-boundedness. Some related results are also presented.
Mean Ergodicity of Power-Bounded Operators in Countably Order Complete Banach Lattices.
Mean lower bounds for Markov operators
Let T be a Markov operator on an L¹-space. We study conditions under which T is mean ergodic and satisfies dim Fix(T) < ∞. Among other things we prove that the sequence converges strongly to a rank-one projection if and only if there exists a function 0 ≠ h ∈ L¹₊ which satisfies for every density f. Analogous results for strongly continuous semigroups are given.
Mean value theorem for convex functionals
Means and Concave Products of Positive Semi-Definite Matrices.