O některých Banachových problémech
On (a,b,c,d)-orthogonality in normed linear spaces
We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.
On Banach spaces X for which
On Biorthogonal Systems and Total Sequences of Functionals. II.
On Carathéodory's and Krein-Milman's theorems in fully ordered groups
On coarse embeddability into -spaces and a conjecture of Dranishnikov
We show that the Hilbert space is coarsely embeddable into any for 1 ≤ p ≤ ∞. It follows that coarse embeddability into ℓ₂ and into are equivalent for 1 ≤ p < 2.
On continuous images of Eberlein compacts
On contraction-type mappings on a 2-normed space
On contradictions of normed vector spaces
On cosine operator functions and one-parameter groups of operators
On Hamel bases in Banach spaces
It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.
On Hilbert sets and -spaces with no subspace isomorphic to
On isometries in linear metric spaces
On Kadec-Klee norms on Banach spaces
On local and global moduli of convexity
On minimal points
On modular sequence spaces
On monotonic functions from the unit interval into a Banach space with uncountable sets of points of discontinuity
We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. We show that if f: [0,1] → X is an increasing function with respect to a norming subset E of X* with uncountably many points of discontinuity and Q is a countable dense subset of [0,1], then (1) contains an order isomorphic copy of D(0,1), (2) contains an isomorphic copy of C([0,1]), (3) contains an isomorphic copy of c₀(Γ) for some uncountable set Γ, (4) if...
On -normed spaces.
On non linear perturbations of isometries.