L’analogue dans des théorèmes de convexité de M. Riesz et G.O. Thorin
L’analogue dans des théorèmes de convexité de M. Riesz et G. O. Thorin
Layer potentials C*-algebras of domains with conical points
To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm...
Les cônes autopolaires en dimension finie
Lie algebras generated by Jordan operators
It is proved that if is a Jordan operator on a Hilbert space with the Jordan decomposition , where is normal and is compact and quasinilpotent, i = 1,2, and the Lie algebra generated by J₁,J₂ is an Engel Lie algebra, then the Banach algebra generated by J₁,J₂ is an Engel algebra. Some results for normal operators and Jordan operators on Banach spaces are given.
Limited -converging operators and relation with some geometric properties of Banach spaces
By using the concepts of limited -converging operators between two Banach spaces and , -sets and -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as -Dunford–Pettis property of order and Pelczyński’s property of order , .
Linear inessential operators and generalized inverses
The space of inessential bounded linear operators from one Banach space into another is introduced. This space, , is a subspace of which generalizes Kleinecke’s ideal of inessential operators. For certain subspaces of , it is shown that when has a generalized inverse modulo , then there exists a projection such that has a generalized inverse and .
Linear maps Lie derivable at zero on 𝒥-subspace lattice algebras
A linear map L on an algebra is said to be Lie derivable at zero if L([A,B]) = [L(A),B] + [A,L(B)] whenever [A,B] = 0. It is shown that, for a 𝒥-subspace lattice ℒ on a Banach space X satisfying dim K ≠ 2 whenever K ∈ 𝒥(ℒ), every linear map on ℱ(ℒ) (the subalgebra of all finite rank operators in the JSL algebra Alg ℒ) Lie derivable at zero is of the standard form A ↦ δ (A) + ϕ(A), where δ is a generalized derivation and ϕ is a center-valued linear map. A characterization of linear maps Lie derivable...
Lineární algebra ukrytá v internetovém vyhledávači Google
Linear-topological classification of matroid C*-algebras.
Little G. T. for lp-lattice summing operators
2000 Mathematics Subject Classification: 46B28, 47D15.In this paper we introduce and study the lp-lattice summing operators in the category of operator spaces which are the analogous of p-lattice summing operators in the commutative case. We study some interesting characterizations of this type of operators which generalize the results of Nielsen and Szulga and we show that Λ l∞( B(H) ,OH) ≠ Λ l2( B( H) ,OH), in opposition to the commutative case.
Local entropy moduli and eigenvalues of operators in Banach spaces.
In the paper local entropy moduli of operators between Banach spaces are introduced. They constitue a generalization of entropy numbers and moduli, and localize these notions in an appropriate way. Many results regarding entropy numbers and moduli can be carried over to local entropy moduli. We investigate relations between local entropy moduli and s-numbers, spectral properties, eigenvalues, absolutely summing operators. As applications, local entropy moduli of identical and diagonal operators...
Local properties of accessible injective operator ideals
In addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a “good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessibility condition (theorem 3.1). This observation leads in a natural way to a characterization of accessible...
Locally compact semi-algebras generated by a commuting operator family.
Locally convex quasi C*-algebras and noncommutative integration
We continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm topology and we focus our attention on the so-called locally convex quasi C*-algebras. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra (𝔛,𝔄₀) can be represented in a class of noncommutative local L²-spaces.
Locally inner derivations of standard operator algebras
It is proved that every locally inner derivation on a symmetric norm ideal of operators is an inner derivation.
Lokaltopologische Vektorräume II.
Lucid operators on Banach spaces
l(Φ,φ) operators and (Φ,φ)-spaces.
A new class of linear and bounded operators is introduced. This class is more general than the classes of operators from [4], [5] and [8]. Using this class lΦ,φ we also introduce a class of locally convex spaces which is more general than the classes of the nuclear spaces [2], [3] and φ-nuclear spaces [6]. For this class of operators similar properties are established to those of the well known classes lp, lφ, lΦ and also the stability of the tensor product is proved. The stability of the tensor...