Duality of Fock spaces with respect to the minimal norm

In this note we prove a duality theorem for generalized Fock spaces.     

Duality theorem for weak L-R smash products

This paper gives a duality theorem for weak L-R smash products, which extends the duality theorem for weak smash products given by Nikshych.     

On triangular norm based axiomatic extensions of the weak nilpotent minimum logic

In this paper we carry out an algebraic investigation of the weak nilpotent minimum logic (WNM) and its t‐norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM‐algebras (?????) and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM‐chains, in particular varieties generated by standard WNM‐chains, or equivalently t‐norm based axiomatic extensions of WNM, and we study their standard completeness properties. We also characterize the generic WNM‐chains, i. e. those that generate the variety ?????, and we give finite axiomatizations for some t‐norm based extensions of WNM. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The norm and the essential norm of the double layer elastic and hydrodynamic potentials in the space of continuous functions

We study a class of matrix integral operators which appear as limit values of the double layer potentials. We find general representations for the norms and for the essential norms of such operators in the space of continuous vector-valued functions. These representations are specified for boundary integral operators of linear isotropic elasticity theory and hydrodynamics of viscous incompressible fluid under the assumption that there is an angle point on the boundary of a plane domain and a conic point or an edge on the boundary of a three-dimensional domain.     

The essential norm of an operator is not self-dual

It is established by an example that the distance of a bounded linear operatorS from the class of compact operators on a Banach space is not always uniformly comparable with that of its adjointS′. This provides a negative solution to an old problem. It is also shown that the seminorms due to Schechter and Weis, that measure the deviation from strict singularity or strict cosingularity of an operator, are not uniformly comparable with the corresponding distance functions. Both results rely on a general construction related to certain approximation properties that are associated with closed ideals of operators.     

On the norm and the essential norm of weighted composition operators acting on the weighted Banach space of analytic functions

The objective of this paper is to use known properties of the associated weight to give new estimations of the norm and essential norm of the weighted com- position operators acting between weighted Banach spaces of analytic functions, in terms of composition with certain special functions in these spaces. As a consequence of our results, we obtain genuine extensions of a large number of recent results, and in particular, we extend classical results due to Montes-Rodríguez and Contreras and Hernández-Díaz.     

Duality and operator algebras: automatic weak* continuity and applications

We investigate some subtle and interesting phenomena in the duality theory of operator spaces and operator algebras, and give several applications of the surprising fact that certain maps are always weak^*-continuous on dual spaces. In particular, if X is a subspace of a C^*-algebra A, and if a∈A satisfies aX⊂X, then we show that the function x?ax on X is automatically weak^* continuous if either (a) X is a dual operator space, or (b) a^*X⊂X and X is a dual Banach space. These results hinge on a generalization to Banach modules of Tomiyama's famous theorem on contractive projections onto a C^*-subalgebra. Applications include a new characterization of the σ-weakly closed (possibly nonunital and nonselfadjoint) operator algebras, and a generalization of the theory of W^*-modules to the framework of modules over such algebras. We also give a Banach module characterization of σ-weakly closed spaces of operators which are invariant under the action of a von Neumann algebra.     

On the essential norm of the Cauchy singular integral operator in weighted rearrangement-invariant spaces

In this paper we extend necessary conditions for Fredholmness of singular integral operators with piecewise continuous coefficients in rearrangement-invariant spaces [19] to the weighted caseX(,w). These conditions are formulated in terms of indices (Q _t w) and (Q _t w) of a submultiplicative functionQ _t w, which is associated with local properties of the space, of the curve, and of the weight at the pointt. Using these results we obtain a lower estimate for the essential norm |S| of the Cauchy singular integral operatorS in reflexive weighted rearrangement-invariant spacesX(,w) over arbitrary Carleson curves :

The essential norm of a composition operator on the bergman space of the unit ball

In this paper, we express the essential norm of a composition operator on Bergman spaces of the unit ball in terms of an asymptotic upper bound of a quantity involving the pull-back measure induced by the inducing map. The result could be generalized to convex domains of finite type and to the weighted situation.     

The essential norm of Hankel operator on the Bergman spaces of strongly pseudoconvex domains

Let D be a bounded strongly pseudoconvex domain with smooth boundary in Cⁿ and let fL²(D). For the Hankel operator H_f on the Bergman space A²(D), it is shown that the essential norm of H_f in L²(D) is comparable to the distance norm from H_f to compact Hankel operators. The result extends the previous corresponding version in the disc proved by Lin and Rochberg in Integ.Equat.Oper.Theory 361–372,17 (1993).     

Gr-Morita对偶与Morita对偶

设G为有单位元e的群R=(?)R_x和A=(?)A_x都是有单位元的G型强分次环,U=(?)U_z是分次(R,A)一双模.本文主要证明了_RU_A导出一个Gr—Morita对偶当且仅当R_eU_(eAc)导出一个Morita对偶.     

Uniform Gateaux differentiability and weak uniform rotundity in Musielak-Orlicz function spaces of Bochner type equipped with the Luxemburg norm

Criteria for weak uniform rotundity and reflexivity of Musielak-Orlicz function spaces of Bochner type equipped with the Luxemburg norm are given. Although, criteria for uniform Gateaux differentiability and weak uniform rotundity of Musielak-Orlicz function spaces of real functions equipped with the Luxemburg norm were known, they can be also easily deduced from our main results.     

A norm equivalence for the mixed norm of Fock type

In this paper, we prove that the mixed norm for an exponential type weighted integral of an entire function is equivalent to the mixed norm of its radial derivative and the distortion function from the weight function in the n-dimensional complex space.     

Strange Duality and Polar Duality

A relation is described between Arnold's strange duality anda polar duality between the Newton polytopes which is mostlydue to M. Kobayashi. It is shown that this relation continuesto hold for the extension of Arnold's strange duality foundby C. T. C. Wall and the author. By a method of Ehlers–Varchenko,the characteristic polynomial of the monodromy of a hypersurfacesingularity can be computed from the Newton diagram. This methodis generalized to the isolated complete intersection singularitiesembraced in the extended duality. This is used to explain theduality of characteristic polynomials of the monodromy discoveredby K. Saito for Arnold's original strange duality and extendedby the author to the other cases.     

Fractional integrals, potential operators and two-weight, weak type norm inequalities on spaces of homogeneous type

We prove two-weight, weak type norm inequalities for potential operators and fractional integrals defined on spaces of homogeneous type. We show that the operators in question are bounded from L^p(v) to L^q,∞(u), 1<p?q<∞, provided the pair of weights (u,v) verifies a Muckenhoupt condition with a “power-bump” on the weight u.     

On a minimal complex norm that extends the real euclidean norm

A minimal extension of the real euclidean norm to ⁿ is introduced and some complex analytic properties of its unit ball are studied.Research supported partially by Fulbright Grant (1986–1987) at Universität Osnabrück-Abteilung Vechta.