Near isometries of spaces of weak * continuous functions, with an application to Bochner spaces
Negative results on the Nash-Moser theorem for Köthe sequences spaces and for spaces of ultradifferentiable functions.
New extension of the variational McShane integral of vector-valued functions
We define the Hake-variational McShane integral of Banach space valued functions defined on an open and bounded subset of -dimensional Euclidean space . It is a “natural” extension of the variational McShane integral (the strong McShane integral) from -dimensional closed non-degenerate intervals to open and bounded subsets of . We will show a theorem that characterizes the Hake-variational McShane integral in terms of the variational McShane integral. This theorem reduces the study of our...
New Gaussian Estimates for Enlarged Balls.
New topological measures on the torus
Recently Entov and Polterovich asked if the Grubb measure was the only symplectic topological measure on the torus. Much to our surprise we discovered a whole new class of intrinsic simple topological measures on the torus, many of which were symplectic.
Nondifferentiable functions, Haar null sets and Wiener measure
Non-linear eigenvalue problems and bifurcations for differentiable multivalued maps
Nonlinear integral operators on C(S,E)
Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property
It is shown that if (S,∑,m) is an atomless finite measure space and X is a Banach space without the Radon-Nikodym property, then the quotient space cabv(∑,m;X)/L¹(m;X) is nonseparable.
Nonstandard Integration Theory in Topological Vector Lattices.
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 .
Normal families of holomorphic functions on infinite-dimensional spaces.
Norm-attaining polynomials and differentiability
We give a polynomial version of Shmul'yan's Test, characterizing the polynomials that strongly attain their norm as those at which the norm is Fréchet differentiable. We also characterize the Gateaux differentiability of the norm. Finally we study those properties for some classical Banach spaces.