On non-equivalent bases and conditional bases in Banach spaces
On Normed Almost Linear Spaces.
On one generalization of weakly compactly generated Banach spaces
On probabilistic normed spaces under .
On quotients of which are quotients of
On rough norms on Banach spaces
On sets of discontinuities of functions continuous on all lines
Answering a question asked by K. C. Ciesielski and T. Glatzer in 2013, we construct a -smooth function on and a closed set nowhere dense in such that there does not exist any linearly continuous function on (i.e., function continuous on all lines) which is discontinuous at each point of . We substantially use a recent full characterization of sets of discontinuity points of linearly continuous functions on proved by T. Banakh and O. Maslyuchenko in 2020. As an easy consequence of our...
On sharp triangle inequalities in Banach spaces. II.
On smooth points of boundaries of open sets
The notions of smooth points of the boundary of an open set and α(·) intrinsically paraconvex sets are introduced. It is shown that for an α(·) intrinsically paraconvex open set the set of smooth points is a dense -set of the boundary.
On Some Extremal Problems in Banach Spaces.
On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space
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. A function is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function with respect to any norming subset there exists a separately increasing function such that the sets of points of discontinuity...
On submultiplicative nonnegative functionals on linear maps of linear finitedimensional normed spaces
On the Classification of Complex Lindenstrauss Spaces.
On the Extension of Continuous Linear Functionals and Best Approximation in Normed Linear Spaces.
On the extremal points of the closed unit balls in some abstract spaces
On the invariant subspace problem in Banach spaces
On the moduli of convexity and smoothness
On the points of multivaluedness of metric projections in separable Banach spaces
On the points of multivaluedness of monotone operators
On the stability of a generalized quadratic and quartic type functional equation in quasi-Banach spaces.