The Identification Problem for the Constantly Attenuated Radon Transform.
The impact of the Radon-Nikodym property on the weak bounded approximation property.
A Banach space X is said to have the weak λ-bounded approximation property if for every separable reflexive Banach space Y and for every compact operator T : X → Y, there exists a net (Sα) of finite-rank operators on X such that supα ||TSα|| ≤ λ||T|| and Sα → IX uniformly on compact subsets of X.We prove the following theorem. Let X** or Y* have the Radon-Nikodym property; if X has the weak λ-bounded approximation property, then for every bounded linear operator T: X → Y, there exists a net (Sα)...
The importance of being Orlicz
The inclusion theorem for multiple summing operators
We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.
The index -transform of generalized functions
In this paper the index transformation
The index for Fredholm elements in a Banach algebra via a trace
We show that the existence of a trace on an ideal in a Banach algebra provides an elegant way to develop the abstract index theory of Fredholm elements in the algebra. We prove some results on the problem of the equality of the nonzero exponential spectra of elements ab and ba and use the index theory to formulate a condition guaranteeing this equality in a quotient algebra.
The index for Fredholm elements in a Banach algebra via a trace II
We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.
The index of projective families of elliptic operators.
The influence of topology to non-linear analysis
The injective hull of an archimedean f-algebra
The inner structure of real extensors in uniform spaces
The instability of nonseparable complete Erdős spaces and representations in ℝ-trees
One way to generalize complete Erdős space is to consider uncountable products of zero-dimensional -subsets of the real line, intersected with an appropriate Banach space. The resulting (nonseparable) complete Erdős spaces can be fully classified by only two cardinal invariants, as done in an earlier paper of the authors together with J. van Mill. As we think this is the correct way to generalize the concept of complete Erdős space to a nonseparable setting, natural questions arise about analogies...
The integral analog of a series with a two-point sum range.
The integral wavelet transform in weighted Sobolev spaces.
The interpolation theorem for holomorphic generalized functions
The intersection convolution of relations and the Hahn-Banach type theorems
By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation can have an...
The intrinsic invariant of an approximately finite dimensional factor and the cocycle conjugacy of discrete amenable group actions.
The inverse spectral radius formula and removability of spectrum
The invertible elements are dense in the irrational rotation C*-algebras.
The isolated ideal of a correspondence associated with a topological quiver.