Non-Standard Analysis And Generalized Functions.
Non-standard characterisations of ideals in C(X).
Nonstandard Integration Theory in Topological Vector Lattices.
Nonstrictly Hyperbolic Nonlinear Systems.
Non-trivial derivations on commutative regular algebras.
Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra S[0,1] of all...
Nontrivial expansions of zero and representation of analytic functions by series of simple fractions.
Nontrivial isometries on alpha).
Nontrivial solution for a nonlocal elliptic transmission problem in variable exponent Sobolev spaces.
Non-uniqueness of topology for algebras of polynomials
Non-universal families of separable Banach spaces
We prove that if 𝓒 is a family of separable Banach spaces which is analytic with respect to the Effros Borel structure and no X ∈ 𝓒 is isometrically universal for all separable Banach spaces, then there exists a separable Banach space with a monotone Schauder basis which is isometrically universal for 𝓒 but not for all separable Banach spaces. We also establish an analogous result for the class of strictly convex spaces.
Non-Vanishing of the Bergman Kernel Function at Boundary Points of Certain Domains in Cn .
Non-weakly supercyclic weighted composition operators.
Norm and lower bounds of operators on weighted sequence spaces
Norm attaining and numerical radius attaining operators.
In this note we discuss some results on numerical radius attaining operators paralleling earlier results on norm attaining operators. For arbitrary Banach spaces X and Y, the set of (bounded, linear) operators from X to Y whose adjoints attain their norms is norm-dense in the space of all operators. This theorem, due to W. Zizler, improves an earlier result by J. Lindenstrauss on the denseness of operators whose second adjoints attain their norms, and is also related to a recent result by C. Stegall...
Norm attaining bilinear forms on C*-algebras
We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.
Norm attaining bilinear forms on .
Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces
For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space of all continuous N-linear forms on X, but there are continuous (N+1)-linear forms on X which cannot be approximated by norm attaining (N+1)-linear forms. Actually,X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.
Norm attaining multilinear forms on .
Norm attaining operators
Norm attaining operators versus bilinear forms.
The well known Bishop-Phelps Theorem asserts that the set of norm attaining linear forms on a Banach space is dense in the dual space [3]. This note is an outline of recent results by Y. S. Choi [5] and C. Finet and the author [7], which clarify the relation between two different ways of extending this theorem.