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Maps on idempotents

Peter Šemrl (2005)

Studia Mathematica

Let X be an infinite-dimensional real or complex Banach space, B(X) the algebra of all bounded linear operators on X, and P(X) ⊂ B(X) the subset of all idempotents. We characterize bijective maps on P(X) preserving commutativity in both directions. This unifies and extends the characterizations of two types of automorphisms of P(X), with respect to the orthogonality relation and with respect to the usual partial order; the latter have been previously characterized by Ovchinnikov. We also describe...

Maps on matrices that preserve the spectral radius distance

Rajendra Bhatia, Peter Šemrl, A. Sourour (1999)

Studia Mathematica

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

Zhaofang Bai, Jinchuan Hou, Zongben Xu (2004)

Studia Mathematica

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.

Maps preserving zero products

J. Alaminos, M. Brešar, J. Extremera, A. R. Villena (2009)

Studia Mathematica

A linear map T from a Banach algebra A into another B preserves zero products if T(a)T(b) = 0 whenever a,b ∈ A are such that ab = 0. This paper is mainly concerned with the question of whether every continuous linear surjective map T: A → B that preserves zero products is a weighted homomorphism. We show that this is indeed the case for a large class of Banach algebras which includes group algebras. Our method involves continuous bilinear maps ϕ: A × A → X (for some Banach space X) with the property...

Marcinkiewicz multipliers of higher variation and summability of operator-valued Fourier series

Earl Berkson (2014)

Studia Mathematica

Let f ∈ V r ( ) ∪ r ( ) , where, for 1 ≤ r < ∞, V r ( ) (resp., r ( ) ) 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...

Marcinkiewicz spaces, commutators and non-commutative geometry

(2011)

Banach Center Publications

Nigel J. Kalton was one of the most eminent guests participating in the Józef Marcinkiewicz Centenary Conference. His contribution to the scientific aspect of the meeting was very essential. Nigel was going to prepare a paper based on his plenary lecture. The editors are completely sure that the paper would be a real ornament of the Proceedings. Unfortunately, Nigel's sudden death totally destroyed editors' hopes and plans. Every mathematician knows how unique were Nigel's mathematical achievements....

Markov operators and n-copulas

P. Mikusiński, M. D. Taylor (2009)

Annales Polonici Mathematici

We extend the definition of Markov operator in the sense of J. R. Brown and of earlier work of the authors to a setting appropriate to the study of n-copulas. Basic properties of this extension are studied.

Mathematical and numerical analysis of radiative heat transfer in semi-transparent media

Yao-Chuang Han, Yu-Feng Nie, Zhan-Bin Yuan (2019)

Applications of Mathematics

This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm...

Currently displaying 21 – 40 of 334