Some new deterministic and random variational inequalities and their applications.
Some open problems in Banach space theory
Some Properties of a Regular Sequence in Hilbert Space.
Some remarkable lines of triangles in real normed spaces and characterizations of inner product structures.
Some remarks on inequalities that characterize inner product spaces.
Special symmetries of Banach spaces isomorphic to Hilbert spaces
We characterize Hilbert spaces among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.
Spectra of the difference, sum and product of idempotents
We give a simple proof of the relation between the spectra of the difference and product of any two idempotents in a Banach algebra. We also give the relation between the spectra of their sum and product.
Spectral type of a polynomial of stationary Gaussian process
Stability of positive part of unit ball in Orlicz spaces
The aim of this paper is to investigate the stability of the positive part of the unit ball in Orlicz spaces, endowed with the Luxemburg norm. The convex set in a topological vector space is stable if the midpoint map , is open with respect to the inherited topology in . The main theorem is established: In the Orlicz space the stability of the positive part of the unit ball is equivalent to the stability of the unit ball.
Strange inner product spaces.
Structural properties and limit behaviour of linear stochastic systems in Hilbert spaces
Studies of some items of the lattice theory in relation to the Hilbert-Hermite space
Subgroups of Hilbert spaces.
Subsequences of frames
Every frame in Hilbert space contains a subsequence equivalent to an orthogonal basis. If a frame is n-dimensional then this subsequence has length (1 - ε)n. On the other hand, there is a frame which does not contain bases with brackets.
Subspace in Hermitean Spaces of Countable Dimension. II.
Subspaces in Hermitean Spaces of Countable Dimension.
Subspaces of ℓ₂(X) and Rad(X) without local unconditional structure
It is shown that if a Banach space X is not isomorphic to a Hilbert space then the spaces ℓ₂(X) and Rad(X) contain a subspace Z without local unconditional structure, and therefore without an unconditional basis. Moreover, if X is of cotype r < ∞, then a subspace Z of ℓ₂(X) can be constructed without local unconditional structure but with 2-dimensional unconditional decomposition, hence also with basis.
Subspaces with a common complement in a Banach space
We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement coincide with those pairs which are isomorphic to a pair of graphs of bounded linear operators between two other Banach spaces. (2) The pairs of subspaces of a Banach space X with a common complement coincide with those pairs for which there exists an involution...
Sufficient conditions for the spectrality of self-affine measures with prime determinant
Let be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.
Superpositions of states and a representation theorem