On higher eigenvalues of variational inequalities
It is shown that every almost linear Pexider mappings , , from a unital -algebra into a unital -algebra are homomorphisms when , and hold for all unitaries , all , and all , and that every almost linear continuous Pexider mappings , , from a unital -algebra of real rank zero into a unital -algebra are homomorphisms when , and hold for all , all and all . Furthermore, we prove the Cauchy-Rassias stability of -homomorphisms between unital -algebras, and -linear...
Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica sul planiquarto , . Qui, è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza .
In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators for which there exists a fundamental decomposition of the Krein space with and invariant under .
We use a non-commutative generalization of the Banach Principle to show that the classical individual ergodic theorem for subsequences generated by means of uniform sequences can be extended to the von Neumann algebra setting.
We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of Banach spaces...
Let be affine mappings of . It is well known that if there exists j ≤ 1 such that for every the composition (1) is a contraction, then for any infinite sequence and any , the sequence (2) is convergent and the limit is independent of z. We prove the following converse result: If (2) is convergent for any and any belonging to some subshift Σ of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every the composition (1) is a contraction. This result...
An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some -type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.