More on reverse triangle inequality in inner product spaces.
-inner product spaces and projections
This paper is a continuation of investigations of -inner product spaces given in [five, six, seven] and an extension of results given in [three] to arbitrary natural . It concerns families of projections of a given linear space onto its -dimensional subspaces and shows that between these families and -inner products there exist interesting close relations.
Numerical radius inequalities for Hilbert -modules
We present a new method for studying the numerical radius of bounded operators on Hilbert -modules. Our method enables us to obtain some new results and generalize some known theorems for bounded operators on Hilbert spaces to bounded adjointable operators on Hilbert -module spaces.
O některých Banachových problémech
On a generalized -inner product and the corresponding Cauchy-Schwarz inequality.
On a lattice characterization of Hilbert spaces
On a superadditivity property of Gram's determinant.
On certain trigonometric sums in several variables.
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 complete-cocomplete subspaces of an inner product space
In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space is complete if and only if there exists a -additive state on , the orthomodular poset of complete-cocomplete subspaces of . We then consider the problem of whether every state on , the class of splitting subspaces of , can be extended to a Hilbertian state on ; we show that for the dense hyperplane (of a separable Hilbert space) constructed by P. Pták and...
On criteria of Blumenthal for inner-product spaces
On generalizations of Grüss inequality in inner product spaces and applications.
On orbits for pairs of operators on an infinite-dimensional complex Hilbert space
On reverses of some inequalities in -inner product spaces.
On semi-inner product spaces, I
On solvability of fourth order operator-diferential equations of elliptic type on weight spaces.
On some global and local geometric properties of Calderón-Lozanovskiĭ spaces
Criteria for full k-rotundity (k ∈ ℕ, k ≥ 2) and uniform rotundity in every direction of Calderón-Lozanovskiĭ spaces are formulated. A characterization of -points in these spaces is also given.
On some properties of Banach operators.
On some properties of Banach operators. II.
On strictly convex and strictly 2-convex 2-normed spaces. II.