Corpus ID: 221533945

On tensor fractions and tensor products in the category of stereotype spaces.

@article{SSAkbarov2020OnTF,
  title={On tensor fractions and tensor products in the category of stereotype spaces.},
  author={S.S.Akbarov},
  journal={arXiv: Functional Analysis},
  year={2020}
}
  • S.S.Akbarov
  • Published 2020
  • Mathematics
  • arXiv: Functional Analysis
We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with the tensor products in the category $\sf{Ste}$ of stereotype spaces. In particular, we give sufficient conditions under which the identity $$ X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle $$ holds, where $\odot$ is the injective tensor product in the category $\sf{Ste}$, $\cdot$, the primary tensor… Expand
1 Citations
Holomorphic duality for countable discrete groups
In 2008, the author proposed a version of duality theory for (not necessarily, Abelian) complex Lie groups, based on the idea of using the Arens-Michael envelope of topological algebra and having anExpand

References

SHOWING 1-10 OF 23 REFERENCES
Continuous and smooth envelopes of topological algebras
Since the time when the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics.Expand
Pontryagin Duality in the Theory of Topological Vector Spaces and in Topological Algebra
The theory of topological vector spaces (TVS), being a foundation of modern functional analysis, is now considered as a completely mature, or, to be more specific, dead mathematical discipline. ThisExpand
Topological Vector Spaces
This chapter presents the most basic results on topological vector spaces. With the exception of the last section, the scalar field over which vector spaces are defined can be an arbitrary,Expand
On holomorphic reflexivity conditions for complex Lie groups.
We consider Akbarov's holomorphic version of the non-commutative Pontryagin duality for a complex Lie group. We prove, under the assumption that $G$ is a Stein group with finitely many components,Expand
A duality for Moore groups
We suggest a new generalization of Pontryagin duality from the category of Abelian locally compact groups to a category which includes all Moore groups, i.e. groups whose irreducible representationsExpand
Holomorphic duality for countable discrete groups
In 2008, the author proposed a version of duality theory for (not necessarily, Abelian) complex Lie groups, based on the idea of using the Arens-Michael envelope of topological algebra and having anExpand
Holomorphic functions of exponential type and duality for stein groups with algebraic connected component of identity
We suggest a generalization of Pontryagin duality from the category of commutative, complex Lie groups to the category of (not necessarily commutative) Stein groups with algebraic connected componentExpand
On continuous duality for Moore groups
In this paper we correct the errors of Yu. N. Kuznetsova’s paper on the continuous duality for Moore groups. In [11] Yu. N. Kuznetsova made an attempt to construct a generalization of the PontryaginExpand
Nuclear Locally Convex Spaces
0. Foundations.- 0.1. Topological Spaces.- 0.2. Metric Spaces.- 0.3. Linear Spaces.- 0.4. Semi-Norms.- 0.5. Locally Convex Spaces.- 0.6. The Topological Dual of a Locally Convex Space.- 0.7. SpecialExpand
Topological Vector Spaces II
§ 14 contains the elementary theory of normed spaces and Banach spaces. A number of classical examples are discussed, to which we shall refer time and again in the later parts of the book.
...
1
2
3
...