On the diagonal of matrix transformations
On the diameter of the Banach-Mazur set
On every subspace of which contains an uncountable -independent set, we construct equivalent norms whose Banach-Mazur distance is as large as required. Under Martin’s Maximum Axiom (MM), it follows that the Banach-Mazur diameter of the set of equivalent norms on every infinite-dimensional subspace of is infinite. This provides a partial answer to a question asked by Johnson and Odell.
On the diametral dimension of weighted spaces of analytic germs
We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces and for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.
On the differences of the consecutive powers of Banach algebra elements
Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstances, we investigate elements in the peripheral spectrum, and give further conclusions, also involving the behaviour of and .
On the differentiability of Lipschitz mappings in Fréchet spaces
On the differentiability of mappings and convex functionals: A correction
On the differentiability of mappings and convex functionals
On the differentiability of mappings in functional spaces
On the differentiability of multivalued mappings. I.
On the differentiability of multivalued mappings. II.
On the differentiability of operators and convex functionals
On the differentiability of the norm in trace classes
On the differential geometry of some classes of infinite dimensional manifolds
Albeverio, Kondratiev, and Röckner have introduced a type of differential geometry, which we call lifted geometry, for the configuration space of any manifold . The name comes from the fact that various elements of the geometry of are constructed via lifting of the corresponding elements of the geometry of . In this note, we construct a general algebraic framework for lifted geometry which can be applied to various “infinite dimensional spaces” associated to . In order to define a lifted...
On the differentiation of convex functions
On the differentiation of convex functions in finite and infinite dimensional spaces
On the differentiation of integrals of functions from Lφ(L)
On the differentiation of integrals of functions from Orlicz classes
On the Dirichlet boundary value problem for nonlinear elliptic partial differential equations in Sobolev power weight spaces
On the Dirichlet problem for functions of the first Baire class
Let be a simplicial function space on a metric compact space . Then the Choquet boundary of is an -set if and only if given any bounded Baire-one function on there is an -affine bounded Baire-one function on such that on . This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set .
On the Dirichlet Problem for Semi-Linear Elliptic Equation with L2-Boundary Data.