Mapping in normed linear spaces and characterization of orthogonality problem of best approximations in 2-norm.
Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces.
For a Banach space X, we show how the existence of a norm-one element u in X and a norm-one continuous bilinear mapping f: X x X --> X satisfying f(x,u) = f(u,x) = x for all x in X, together with some more intrinsic conditions, can be utilized to characterize X as a member of some relevant subclass of the class of Banach spaces.
On a characterisation of inner product spaces.
On a functional-analysis approach to orthogonal sequences problems.
Sea T un operador lineal acotado e inyectivo de un espacio de Banach X en un espacio de Hilbert H con rango denso y sea {xn} ⊂ X una sucesión tal que {Txn} es ortogonal. Se estudian propiedades de {Txn} dependientes de propiedades de {xn}. También se estudia la ""situación opuesta"", es decir, la acción de un operador T : H → X sobre sucesiones ortogonales.
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 moduli of expansion of the duality mapping of smooth Banach spaces.
On Solèr's characterization of Hilbert spaces.
On the -angle and -angle in normed spaces.
On the volume method in the study of Auerbach bases of finite-dimensional normed spaces
In this note we show that if the ratio of the minimal volume V of n-dimensional parallelepipeds containing the unit ball of an n-dimensional real normed space X to the maximal volume v of n-dimensional crosspolytopes inscribed in this ball is equal to n!, then the relation of orthogonality in X is symmetric. Hence we deduce the following properties: (i) if V/v=n! and if n>2, then X is an inner product space; (ii) in every finite-dimensional normed space there exist at least two different Auerbach...
Planarizable supersymmetric quantum toboggans.
Quantized orthonormal systems: A non-commutative Kwapień theorem
The concepts of Riesz type and cotype of a given Banach space are extended to a non-commutative setting. First, the Banach space is replaced by an operator space. The notion of quantized orthonormal system, which plays the role of an orthonormal system in the classical setting, is then defined. The Fourier type and cotype of an operator space with respect to a non-commutative compact group fit in this context. Also, the quantized analogs of Rademacher and Gaussian systems are treated. All this is...
Radial projections of bisectors in Minkowski spaces.
Rectangular modulus and geometric properties of normed spaces.
Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces
Some characterizations of inner product spaces in terms of Birkhoff orthogonality are given. In this connection we define the rectangular modulus of the normed space . The values of the rectangular modulus at some noteworthy points are well-known constants of . Characterizations (involving of inner product spaces of dimension , respectively , are given and the behaviour of is studied.
Regards sur le problème des rotations de Mazur.
Sesquilinear and Quadratic Forms on Modules Over *-algebras
Sesquilinear-orthogonally quadratic mappings.
Some characteristic and non-characteristic properties of inner product spaces
Some generalization of Steinhaus' lattice points problem
Steinhaus' lattice points problem addresses the question of whether it is possible to cover exactly n lattice points on the plane with an open ball for every fixed nonnegative integer n. This paper includes a theorem which can be used to solve the general problem of covering elements of so-called quasi-finite sets in Hilbert spaces. Some applications of this theorem are considered.
Some remarks on inequalities that characterize inner product spaces.