Descriptor: "Banach-Lie algebra" - Searchworks@Jio Institute Digital Library Search Results

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Author: Beltiţă, Daniel, Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Coburn, L. A., editor, Davidson, K. R., editor, Douglas, R. G., editor, Dijksma, A., editor, Dym, H., editor, Fuhrmann, P. A., editor, Goldberg, S., editor, Gramsch, B., editor, Heinig, G., editor, Helton, J. A., editor, Kaashoek, M. A., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lancaster, P., editor, Lerer, L. E., editor, Mityagin, B., editor, Peller, V. V., editor, Rodman, L., editor, Rovnyak, J., editor, Sarason, D. E., editor, Spitkovsky, I. M., editor, Treil, S., editor, Upmeier, H., editor, Verduyn, S. M., editor, Voiculescu, D., editor, Widom, H., editor, Xia, D., editor, Yafaev, D., editor, Foias, C., editor, Halmos, P. R., editor, Kailath, T., editor, Lax, P. D., editor, Livsic, M. S., editor, Gaşpar, Dumitru, editor, Timotin, Dan, editor, Zsidó, László, editor, Gohberg, Israel, editor, and Vasilescu, Florian-Horia, editor
Published: 2005
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Author: Biagi, S. and Bonfiglioli, A.
Subjects: *STOCHASTIC convergence, *FRACTAL dimensions, *MATHEMATICAL series, *INFINITY (Mathematics), *BANACH algebras, *LIE algebras, *MATHEMATICAL proofs
Abstract: We prove a convergence result for the Campbell–Baker–Hausdorff–Dynkin seriesin infinite-dimensional Banach–Lie algebras. In the existing literature, this topic has been investigated whenis the Lie algebra of a finite-dimensional Lie group(see [Blanes and Casas, 2004]) or of an infinite-dimensional Banach–Lie group(see [Mérigot, 1974]). Indeed, one can obtain a suitable ODE for, which follows from the well-behaved formulas for the differential of the Exponential Map of the Lie group. The novelty of our approach is to derive this ODE in any infinite-dimensional Banach–Lie algebra, not necessarily associated to a Lie group, as a consequence of an analogous abstract ODE first obtained in the most natural algebraic setting: that of the formal power series in two commuting indeterminatesover the free unital associative algebra generated by two non-commuting indeterminates. [ABSTRACT FROM AUTHOR]
Published: 2014
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Author: Dosiev, Anar
Subjects: *SPECTRUM analysis, *MATHEMATICAL analysis, *FUNCTIONAL analysis, *BANACH spaces
Abstract: Abstract: In this paper, we prove Slodkowski version of the infinite-dimensional spectral mapping theorem and Cartan–Slodkowski version of the finite-dimensional spectral mapping theorem for nilpotent operator Lie subalgebras with respect to the various noncommutative functional calculi. [Copyright &y& Elsevier]
Published: 2006
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Author: Andrea Bonfiglioli, Stefano Biagi, S Biagi, and A Bonfiglioli
Subjects: Discrete mathematics, Pure mathematics, Algebra and Number Theory, Campbell-Baker-Hausdorff-Dynkin Theorem, Simple Lie group, Banach-Lie algebra, Banach–Lie algebra, Campbell–Baker–Hausdorff–Dynkin Theorem, domain of convergence, formal power series, Affine Lie algebra, Exponential map (Lie theory), Graded Lie algebra, Lie conformal algebra, Adjoint representation of a Lie algebra, Representation of a Lie group, Lie algebra, Mathematics
Abstract: We prove a convergence result for the Campbell–Baker–Hausdorff–Dynkin series in infinite-dimensional Banach–Lie algebras L. In the existing literature, this topic has been investigated when L is the Lie algebra Lie(G) of a finite-dimensional Lie group G (see [Blanes and Casas, 2004]) or of an infinite-dimensional Banach–Lie group G (see [Mérigot, 1974]). Indeed, one can obtain a suitable ODE, which follows from the well-behaved formulas for the differential of the Exponential Map of the Lie group G. The novelty of our approach is to derive this ODE in any infinite-dimensional Banach–Lie algebra, not necessarily associated to a Lie group, as a consequence of an analogous abstract ODE first obtained in the most natural algebraic setting: that of the formal power series in two commuting indeterminates over the free unital associative algebra generated by two non-commuting indeterminates.
Published: 2014

Author: Anar Dosiev
Subjects: Unbounded operator, Pure mathematics, Adjoint representation, Cartan subalgebra, Cartan–Slodkowski spectra, Parametrized Banach space complex, Noncommutative geometry, Algebra, Banach–Lie algebra, Uniform boundedness principle, Nilpotent operator, Mathematics::Quantum Algebra, Open mapping theorem (functional analysis), Bounded inverse theorem, Mathematics::Representation Theory, Analysis, Mathematics
Abstract: In this paper, we prove Slodkowski version of the infinite-dimensional spectral mapping theorem and Cartan–Slodkowski version of the finite-dimensional spectral mapping theorem for nilpotent operator Lie subalgebras with respect to the various noncommutative functional calculi.
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