Embeddings into $\mathbb{B}$-cyclic Banach spaces
Vladikavkazskij matematičeskij žurnal, Tome 24 (2022) no. 4, pp. 127-132
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For a complete Boolean algebra $\mathbb{B}$ and nonzero $\pi\in \mathbb{B}$, the notion of an $\mathbb{B}_{\pi}$-embedding of Banach spaces into $\mathbb{B}$-cyclic Banach spaces is introduced. The notion of a lattice $\mathbb{B}_{\pi}$-embedding of Banach lattices into $\mathbb{B}$-cyclic Banach lattices is also introduced. A criterion for the $\mathbb{B}_{\pi}$-embedding of a space of conti-\eject nuous vector-valued functions with values in an arbitrary Banach space into a $\mathbb{B}$-cyclic Banach space is established, as well as a criterion for the lattice $\mathbb{B}_{\pi}$-embedding of a space of continuous vector-valued functions with values in an arbitrary Banach lattice into a $\mathbb{B}$-cyclic Banach lattice. The obtained results allow us to outline an approach for isometric and isomorphic classification of $\mathbb{B}$-cyclic Banach spaces. In the course of establishing the results, the tool of lattice-valued spaces was widely used.
@article{VMJ_2022_24_4_a10,
author = {B. B. Tasoev},
title = {Embeddings into $\mathbb{B}$-cyclic {Banach} spaces},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {127--132},
year = {2022},
volume = {24},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2022_24_4_a10/}
}
B. B. Tasoev. Embeddings into $\mathbb{B}$-cyclic Banach spaces. Vladikavkazskij matematičeskij žurnal, Tome 24 (2022) no. 4, pp. 127-132. http://geodesic.mathdoc.fr/item/VMJ_2022_24_4_a10/