An extension theorem to rough paths
An extremal problem in Banach algebras
We study asymptotics of a class of extremal problems rₙ(A,ε) related to norm controlled inversion in Banach algebras. In a general setting we prove estimates that can be considered as quantitative refinements of a theorem of Jan-Erik Björk [1]. In the last section we specialize further and consider a class of analytic Beurling algebras. In particular, a question raised by Jan-Erik Björk in [1] is answered in the negative.
An ideal boundary for domains in -space.
An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property
C.-M. Cho and W. B. Johnson showed that if a subspace E of , 1 < p < ∞, has the compact approximation property, then K(E) is an M-ideal in ℒ(E). We prove that for every r,s ∈ ]0,1] with , the James space can be provided with an equivalent norm such that an arbitrary subspace E has the metric compact approximation property iff there is a norm one projection P on ℒ(E)* with Ker P = K(E)⊥ satisfying ∥⨍∥ ≥ r∥Pf∥ + s∥φ - Pf∥ ∀⨍ ∈ ℒ(E)*. A similar result is proved for subspaces of upper p-spaces...
An identity for reproducing kernels in a planar domain and Hilbert-Schmidt Hankel operators.
An identity in real inner product spaces.
An ill-posed nonlocal two-point problem for systems of partial differential equations.
An imbedding theorem for H°(G,Ω)-spaces
An implicit function theorem in Banach spaces
An indecomposable and unconditionally saturated Banach space
We construct an indecomposable reflexive Banach space such that every infinite-dimensional closed subspace contains an unconditional basic sequence. We also show that every operator is of the form λI + S with S a strictly singular operator.
An indecomposable Banach space of continuous functions which has small density
Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.
An index formula for chains
We derive a formula for the index of Fredholm chains on normed spaces.
An index theorem for systems of difference operators on a half space
An individual ergodic theorem on the Hilbert space logic
An inequality between the James and James type constants in Banach spaces
We consider the James and Schäffer type constants recently introduced by Takahashi. We prove an equality between James (resp. Schäffer) type constants and the modulus of convexity (resp. smoothness). By using these equalities, we obtain some estimates for the new constants in terms of the James constant. As a result, we improve an inequality between the Zbăganu and James constants.
An inequality for bi-orthogonal pairs.
An inequality for the indefinite integral of a function in
An inequality improving the first Hermite-Hadamard inequality for convex functions defined on linear spaces and applications for semi-inner products.
An inequality in Orlicz function spaces with Orlicz norm
We use Simonenko quantitative indices of an -function to estimate two parameters and in Orlicz function spaces with Orlicz norm, and get the following inequality: , where and are Simonenko indices. A similar inequality is obtained in with Orlicz norm.
An Inequality Related to the Uniform Convexity in Banach Spaces