The theory of bounding subsets of topological vector spaces without convexity condition
The theory of Marcinkiewicz-Orlicz spaces [Book]
The theory of stationary vector-valued measures over R.
The three point pick problem on the bidisk.
The three space problem for locally bounded -spaces
The three space problem for smooth partitions of unity and C(K) spaces.
The three-space-problem for locally-m-convex algebras.
We prove that a locally convex algebra A with jointly continuous multiplication is already locally-m-convex, if A contains a two-sided ideal I such that both I and the quotient algebra A/I are locally-m-convex. An application to the behaviour of the associated locally-m-convex topology on ideals is given.
The Tomita operator for the free scalar field
The topological complexity of sets of convex differentiable functions.
Let C(X) be the set of all convex and continuous functions on a separable infinite dimensional Banach space X, equipped with the topology of uniform convergence on bounded subsets of X. We show that the subset of all convex Fréchet-differentiable functions on X, and the subset of all (not necessarily equivalent) Fréchet-differentiable norms on X, reduce every coanalytic set, in particular they are not Borel-sets.
The topological product structure of systems of Lebesgue spaces.
The topological proof of the Nachbin-Shirota's theorem
The topological snake lemma and corona algebras.
The topology of the Banach–Mazur compactum
Let J(n) be the hyperspace of all centrally symmetric compact convex bodies , n ≥ 2, for which the ordinary Euclidean unit ball is the ellipsoid of maximal volume contained in A (the John ellipsoid). Let be the complement of the unique O(n)-fixed point in J(n). We prove that: (1) the Banach-Mazur compactum BM(n) is homeomorphic to the orbit space J(n)/O(n) of the natural action of the orthogonal group O(n) on J(n); (2) J(n) is an O(n)-AR; (3) is an Eilenberg-MacLane space ; (4) is noncontractible;...
The trace class is a -algebra.
The trace in semi-finite von Neumann algebras.
The trace of finite and nuclear elements in Banach algebras
The trace of Sobolev and Besov spaces if 0 < p < 1
The Trace of Sobolev-Slobodeckij spaces on Lipschitz domains.
The trace theorem revisited
Filling a possible gap in the literature, we give a complete and readable proof of this trace theorem, which also shows that the imbedding constant is uniformly bounded for . The proof is based on a version of Hardy’s inequality (cp. Appendix).
The Trace to the Boundary of Sobolev spaces on a snowflake.