8 citations · 27 across the 14 of their papers we have counts for
12 papers · 1 filter
Real-analytic functional calculus and strictly real Banach algebras
Oleg Aristov
We use real-analytic functional calculus to show that the envelope of the algebra of -variable polynomials with real coefficients, with respect to the class of strictly real Ban…
Finitely -generated associative and Hopf algebras
Oleg Aristov
We introduce finitely -generated algebras, which can be treated as `algebras of functions' on non-commutative -differentiable spaces. Our approach uses the cate…
On density of polynomials in the algebra of holomorphic functions of exponential type on a linear Lie group
Oleg Aristov
It is shown by the author in [J. Lie Theory 29:4, 1045-1070, 2019] that for every connected linear complex Lie group the algebra of polynomials (regular functions) is dense in the…
Decomposition of the algebra of analytic functionals on a connected complex Lie group and its completions into iterated analytic smash products
Oleg Aristov
We show that a decomposition of a complex Lie group into a semidirect product generates that of the algebra of analytic functional, , into an analytic smash pr…
Length functions exponentially distorted on subgroups of complex Lie groups
Oleg Aristov
We introduce a notion of a length function exponentially distorted on a (compactly generated) subgroup of a locally compact group. We prove that for a connected linear complex Lie…
Functions of class in non-commuting variables in the context of triangular Lie algebras
Oleg Aristov
We construct a certain completion of the universal enveloping algebra of a triangular real Lie algebra . It is a Fréchet-Arens-Michael algebra…
Holomorphically finitely generated Hopf algebras and quantum Lie groups
Oleg Aristov
We study topological Hopf algebras that are holomorphically finitely generated (HFG) as Fréchet Arens--Micheal algebras in the sense of Pirkovskii. Some of them, but not all, can b…
On holomorphic reflexivity conditions for complex Lie groups
Oleg Aristov
We consider Akbarov's holomorphic version of the non-commutative Pontryagin duality for a complex Lie group. We prove, under the assumption that is a Stein group with finitely…
The relation "commutator equals function'' in Banach algebras
Oleg Aristov
The relation , where is a holomorphic function, occurs naturally in the definitions of some quantum groups. To attach a rigorous meaning to the right-hand side of t…
Arens-Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms
Oleg Aristov
Our aim is to give an explicit description of the Arens-Michael envelope for the universal enveloping algebra of a finite-dimensional nilpotent complex Lie algebra. It turns out th…
Topological radical of Banach module
Oleg Aristov
We introduce the concept of topological radical of a Banach module. This closed submodule have two description: the as the intersection of ranges of maximal contractive monomorphis…
Operator biflatness of the Fourier algebra and approximate indicators for subgroups
Oleg Yu. Aristov, Volker Runde, Nico Spronk
We investigate if, for a locally compact group , the Fourier algebra is biflat in the sense of quantized Banach homology. A central role in our investigation is played by…