A structure theorem Lie algebras of unbounded derivations in -algebras
A structure theory for Jordan -pairs
Jordan -pairs appear, in a natural way, in the study of Lie -triple systems ([3]). Indeed, it is shown in [4, Th. 3.1] that the problem of the classification of Lie -triple systems is reduced to prove the existence of certain -algebra envelopes, and it is also shown in [3] that we can associate topologically simple nonquadratic Jordan -pairs to a wide class of Lie -triple systems and then the above envelopes can be obtained from a suitable classification, in terms of associative -pairs, of...
A study of various results for a class of entire Dirichlet series with complex frequencies
Let be a class of entire functions represented by Dirichlet series with complex frequencies for which is bounded. Then is proved to be a commutative Banach algebra with identity and it fails to become a division algebra. is also proved to be a total set. Conditions for the existence of inverse, topological zero divisor and continuous linear functional for any element belonging to have also been established.
A study on some new types of Hardy-Hilbert's integral inequality.
A subelliptic Bourgain–Brezis inequality
We prove an approximation lemma on (stratified) homogeneous groups that allows one to approximate a function in the non-isotropic Sobolev space by functions, generalizing a result of Bourgain–Brezis. We then use this to obtain a Gagliardo–Nirenberg inequality for on the Heisenberg group .
A subfield of a complex Banach algebra is not necessarily topologically isomorphic to a subfield of ℂ
A sub-regularity inequality for conjugate systems on local fields
A subsequence characterization of sequences spanning isomorphically polyhedral Banach spaces
Let (x_n) be a sequence in a Banach space X which does not converge in norm, and let E be an isomorphically precisely norming set for X such that (*) ∑_n |x*(x_{n+1} - x_n)| < ∞, ∀x* ∈ E. Then there exists a subsequence of (x_n) which spans an isomorphically polyhedral Banach space. It follows immediately from results of V. Fonf that the converse is also true: If Y is a separable isomorphically polyhedral Banach space then there exists a normalized M-basis (x_n) which spans Y and there exists...
A sufficient condition of type (...) for Tame Splitting of short exact sequences of Fréchet spaces.
A summability condition on the gradient ensuring BMO.
A Supplement to a Theorem of T. Ando.
A survey of recent reverses for the generalised triangle inequality in inner product spaces
A survey of weighted substitution operators and generalizations of Banach--Stone theorem.
A survey on dilations of projective isometric representations.
A survey on representations of the unitary group U(∞)
A survey on tent spaces and their application to weighted inequalities
A survey on the classification of factors of von Neumann algebras.
A survey on the general central limit problem in Banach spaces
A survey on the numerical index of a Banach space.
A survey on the Szlenk index and some of its applications.
We describe how the Szlenk index has been used in various areas of the geometry of Banach spaces. We cover the following domains of application of this notion: non existence of universal spaces, linear classification of C(K) spaces, descriptive set theory, renorming problems and non linear classification of Banach spaces.