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...