58 research outputs found
Decompositions of Nakano norms by ODE techniques
We study decompositions of Nakano type varying exponent Lebesgue norms and
spaces. These function spaces are represented here in a natural way as
tractable varying sums of projection bands. The main results involve
embedding the varying Lebesgue spaces to such sums, as well as the
corresponding isomorphism constants. The main tool applied here is an
equivalent variable Lebesgue norm which is defined by a suitable ordinary
differential equation introduced recently by the author. We also analyze the
effect of transformations changing the ordering of the unit interval on the
values of the ODE-determined norm
Note on order-isomorphic isometric embeddings of some recent function spaces
We investigate certain recently introduced ODE-determined varying exponent
spaces. It turns out that these spaces are finitely representable in a
concrete universal varying exponent space. Moreover, this can be
accomplished in a natural unified fashion. This leads to order-isomorphic
isometric embeddings of all of the above spaces to an ultrapower of the
above varying exponent space
Extracting long basic sequences from systems of dispersed vectors
We study Banach spaces satisfying some geometric or structural properties
involving tightness of transfinite sequences of nested linear subspaces. These
properties are much weaker than WCG and closely related to Corson's property
(C). Given a transfinite sequence of normalized vectors, which is dispersed or
null in some sense, we extract a subsequence which is a biorthogonal sequence,
or even a weakly null monotone basic sequence, depending on the setting. The
Separable Complementation Property is established for spaces with an M-basis
under rather weak geometric properties. We also consider an analogy of the
Baire Category Theorem for the lattice of closed linear subspaces.Comment: 17 page
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