A graph property G is a collection of graphs closed under isomorphism. G is said to be evasive if, for every possible local search strategy, there is at least one graph for which membership in G cannot be decided until the entire graph has been searched. Most graph properties that one can think of, but not all, turn out to be evasive. A conjecture of Aanderaa, Karp and Rosenberg asserts that ev...

Continuing the research on the Banach-Saks and Schur properties started in (cf. [10]) we investigate analogous properties in the module context. As an environment serves the class of Hilbert C∗-modules. Some properties of weak module topologies on Hilbert C∗-modules are described. Natural module analogues of the classical weak Banach-Saks and the classical Schur properties are defined and studi...

A characterization of Haar null sets in the sense of Christensen is given. Using it, we show that if the dual of a Banach space X has the Banach-Saks property, then closed and convex subsets of X with empty interior are Haar null.

In this paper we show the weak Banach-Saks property of the Banach vector space (L p µ) m generated by m L p µ-spaces for 1 ≤ p < +∞, where m is any given natural number. When m = 1, this is the famous Banach-Saks-Szlenk theorem. By use of this property, we also present inequalities for integrals of functions that are the composition of nonnegative continuous convex functions on a convex set of ...

Motivated by the equivalent definition of a continuous operator between Banach spaces in terms weakly null nets, we introduce unbounded operators replacing weak convergence with absolutely (uaw-convergence) lattices. We characterize order lattices and reflexive these operators. Moreover, motivated characterizing lattice Cauchy sequences, consider pre-unbounded which maps uaw-Cauchy sequences to...

Abstract Using the Bessaga–Pełczyński selection principle, we give an alternative and concise proof of results obtained by Tu (Arch Math, 117:315–322, 2021) that several quantities defined for bounded subsets Banach spaces related to compactness, weak Banach–Saks property coincide in $$l_{1}$$ l 1</mml...