A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev Space
A note on complemented Banach *-algebras.
A note on complex interpolation of Banach lattices
We complete a result of Hernandez on the complex interpolation for families of Banach lattices.
A note on complex -predual spaces.
A note on composition operators on spaces of real analytic functions
We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.
A note on comprehensive backward biorthogonalization.
A note on continuous restrictions of linear maps between Banach spaces.
A note on convergence of level sets.
A note on copies of in spaces of weak* measurable functions
If is a finite measure space and a Banach space, in this note we show that , the Banach space of all classes of weak* equivalent -valued weak* measurable functions defined on such that a.e. for some equipped with its usual norm, contains a copy of if and only if contains a copy of .
A Note on cotype of smooth spaces.
A note on criteria of Le Page and Hirschfeld-Żelazko for the commutativity of Banach algebras
A note on derivations of algebras of analytic functions.
A Note on Differentiability of Lipschitz Maps
We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
A note on Dirac operators on the quantum punctured disk.
A note on direct sum of ordered topological vector spaces
A note on distribution spaces on manifolds.
A Note on Div-Curl Lemma
2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and which include as a particular case, the result of [3].
A note on dual Banach spaces.
A note on Dunford-Pettis like properties and complemented spaces of operators
Equivalent formulations of the Dunford-Pettis property of order (), , are studied. Let , , , , and denote respectively the sets of all bounded linear, weakly compact, compact, unconditionally converging, and -convergent operators from to . Classical results of Kalton are used to study the complementability of the spaces and in the space , and of in and .
A note on embedding into product spaces
Using factorization properties of an operator ideal over a Banach space, it is shown how to embed a locally convex space from the corresponding Grothendieck space ideal into a suitable power of , thus achieving a unified treatment of several embedding theorems involving certain classes of locally convex spaces.