scholarly journals Analytic joint spectral radius in a solvable Lie algebra of operators

2001 ◽  
Vol 144 (2) ◽  
pp. 153-167
Author(s):  
Daniel Beltiţă
Keyword(s):  
Lie Algebra ◽  
Spectral Radius ◽  
Joint Spectral Radius ◽  
Solvable Lie Algebra ◽  
Algebra Of Operators

Symbols in Berezin quantization for representation operators

2021 ◽  
pp. 296-304
Author(s):  
Vladimir F. Molchanov ◽  
Svetlana V. Tsykina
Keyword(s):  
Homogeneous Space ◽  
Lie Algebra ◽  
Grassmann Manifold ◽  
Homogeneous Spaces ◽  
Finite Multiplicity ◽  
Basic Notion ◽  
Berezin Quantization ◽  
Algebraic Version ◽  
Enveloping Algebra ◽  
Algebra Of Operators

The basic notion of the Berezin quantization on a manifold M is a correspondence which to an operator A from a class assigns the pair of functions F and F^♮ defined on M. These functions are called covariant and contravariant symbols of A. We are interested in homogeneous space M=G/H and classes of operators related to the representation theory. The most algebraic version of quantization — we call it the polynomial quantization — is obtained when operators belong to the algebra of operators corresponding in a representation T of G to elements X of the universal enveloping algebra Env g of the Lie algebra g of G. In this case symbols turn out to be polynomials on the Lie algebra g. In this paper we offer a new theme in the Berezin quantization on G/H: as an initial class of operators we take operators corresponding to elements of the group G itself in a representation T of this group. In the paper we consider two examples, here homogeneous spaces are para-Hermitian spaces of rank 1 and 2: a) G=SL(2;R), H — the subgroup of diagonal matrices, G/H — a hyperboloid of one sheet in R^3; b) G — the pseudoorthogonal group SO_0 (p; q), the subgroup H covers with finite multiplicity the group SO_0 (p-1,q -1)×SO_0 (1;1); the space G/H (a pseudo-Grassmann manifold) is an orbit in the Lie algebra g of the group G.

scholarly journals Lifted Polytope Methods for Computing the Joint Spectral Radius

2014 ◽  
Vol 35 (2) ◽  
pp. 391-410 ◽  
Author(s):  
Raphaël M. Jungers ◽  
Antonio Cicone ◽  
Nicola Guglielmi
Keyword(s):  
Spectral Radius ◽  
Joint Spectral Radius
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