Smooth Homogeneous Structures in Operator Theory

Beltiţă, Daniel

doi:10.1201/9781420034806

Cited by 35 publications

(63 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is easy to see that B × ⊆ KAN; hence g = kb ∈ KAN = m(K × A × N ). The fact that K, A, N are Banach-Lie groups with the corresponding Lie algebras k, a, and n, respectively, follows for instance by Corollary 3.7 in [Be06], and in addition the inclusion maps of K, A, and N into G are smooth. It then follows that the multiplication map m : K × A × N → G is smooth as well.…”

Section: N) → Kan Is Smooth and Bijective • The Mapping M Is A Dimentioning

confidence: 99%

“…By the hypothesis that g 0 is an elliptic Banach-Lie algebra, it follows that ad g 0 X : g 0 → g 0 is a Hermitian operator (see Definition 5.23 in [Be06]). If g stands for the complexification of g 0 , then ad g X : g → g is Hermitian as well.…”

Section: Iwasawa Decompositions For Involutive Banach-lie Groupsmentioning

confidence: 99%

“…The maps Ψ adg 0 X and Ψ adgX can be constructed by the Weyl functional calculus as in Example 5.25 in [Be06]. Now let ι : g 0 → g be the inclusion map.…”

Section: Iwasawa Decompositions For Involutive Banach-lie Groupsmentioning

confidence: 99%

See 2 more Smart Citations

Iwasawa decompositions of some infinite-dimensional Lie groups

Beltiţă

2009

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

Section: N) → Kan Is Smooth and Bijective • The Mapping M Is A Dimentioning

confidence: 99%

Section: Iwasawa Decompositions For Involutive Banach-lie Groupsmentioning

confidence: 99%

See 1 more Smart Citation

Iwasawa decompositions of some infinite-dimensional Lie groups

Beltiţă

2009

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…It is a real Banach-Lie group with the topology defined by the metric (U 1 , U 2 ) → U 1 − U 2 I (see [5]). The Lie algebra of U(H) I is given by I ah = { A ∈ I : A * = −A }.…”

Section: U(h) I = { U ∈ U(h) : U − I ∈ I }mentioning

confidence: 99%

Geometry of $\mathfrak {I}$-Stiefel manifolds

Chiumiento

2010

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. Let I be a separable Banach ideal in the space of bounded operators acting in a Hilbert space H and U(H) I the Banach-Lie group of unitary operators which are perturbations of the identity by elements in I. In this paper we study the geometry of the unitary orbitswhere V is a partial isometry. We give a spatial characterization of these orbits. It turns out that both are included in V + I, and while the first one consists of partial isometries with the same kernel of V , the second is given by partial isometries such that their initial projections and V * V have null index as a pair of projections. We prove that they are smooth submanifolds of the affine Banach space V + I and homogeneous reductive spaces of U(H) I and U(H) I × U(H) I respectively. Then we endow these orbits with two equivalent Finsler metrics, one provided by the ambient norm of the ideal and the other given by the Banach quotient norm of the Lie algebra of U(H) I (or U(H) I × U(H) I ) by the Lie algebra of the isotropy group of the natural actions. We show that they are complete metric spaces with the geodesic distance of these metrics.

show abstract

“…[Mil83], [Bel06], [GN06]). In this context, the unit groups of continuous inverse algebras are the prototypical "linear Lie groups" ( [Gl02]), and it is a natural question whether the notion of "linearity" in this general context determines a larger class of finite-dimensional Lie groups than the Lie groups of matrices.…”

mentioning

confidence: 99%

Finite-dimensional Lie subalgebras of algebras with continuous inversion

Beltiţă

Neeb

2008

Studia Math.

View full text Add to dashboard Cite

Abstract. We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute modulo the Jacobson radical.

show abstract

Smooth Homogeneous Structures in Operator Theory

Cited by 35 publications

References 0 publications

Iwasawa decompositions of some infinite-dimensional Lie groups

Iwasawa decompositions of some infinite-dimensional Lie groups

Geometry of $\mathfrak {I}$-Stiefel manifolds

Finite-dimensional Lie subalgebras of algebras with continuous inversion

Contact Info

Product

Resources

About