Page 1 Next

Displaying 1 – 20 of 21

Showing per page

Algebra of multipliers on the space of real analytic functions of one variable

Paweł Domański, Michael Langenbruch (2012)

Studia Mathematica

We consider the topological algebra of (Taylor) multipliers on spaces of real analytic functions of one variable, i.e., maps for which monomials are eigenvectors. We describe multiplicative functionals and algebra homomorphisms on that algebra as well as idempotents in it. We show that it is never a Q-algebra and never locally m-convex. In particular, we show that Taylor multiplier sequences cease to be so after most permutations.

Finite sections of truncated Toeplitz operators

Steffen Roch (2015)

Concrete Operators

We describe the C*-algebra associated with the finite sections discretization of truncated Toeplitz operators on the model space K2u where u is an infinite Blaschke product. As consequences, we get a stability criterion for the finite sections discretization and results on spectral and pseudospectral approximation.

K-theory of Boutet de Monvel's algebra

Severino T. Melo, Ryszard Nest, Elmar Schrohe (2003)

Banach Center Publications

We consider the norm closure 𝔄 of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact manifold X with boundary ∂X. Assuming that all connected components of X have nonempty boundary, we show that K₁(𝔄) ≃ K₁(C(X)) ⊕ ker χ, where χ: K₀(C₀(T*Ẋ)) → ℤ is the topological index, T*Ẋ denoting the cotangent bundle of the interior. Also K₀(𝔄) is topologically determined. In case ∂X has torsion free K-theory, we get K₀(𝔄) ≃ K₀(C(X)) ⊕ K₁(C₀(T*Ẋ)).

Layer potentials C*-algebras of domains with conical points

Catarina Carvalho, Yu Qiao (2013)

Open Mathematics

To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm...

On spectrality of the algebra of convolution dominated operators

Gero Fendle, Karlheinz Gröchenig, Michael Leinert (2007)

Banach Center Publications

If G is a discrete group, the algebra CD(G) of convolution dominated operators on l²(G) (see Definition 1 below) is canonically isomorphic to a twisted L¹-algebra l ¹ ( G , l ( G ) , T ) . For amenable and rigidly symmetric G we use this to show that any element of this algebra is invertible in the algebra itself if and only if it is invertible as a bounded operator on l²(G), i.e. CD(G) is spectral in the algebra of all bounded operators. For G commutative, this result is known (see [1], [6]), for G noncommutative discrete...

On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane

Wojciech Młocek, Marek Ptak (2013)

Czechoslovak Mathematical Journal

The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L spaces on the unit circle and the real line...

Projections onto the spaces of Toeplitz operators

Marek Ptak (2005)

Annales Polonici Mathematici

Projections onto the spaces of all Toeplitz operators on the N-torus and the unit sphere are constructed. The constructions are also extended to generalized Toeplitz operators and applied to show hyperreflexivity results.

Rankin–Cohen brackets and representations of conformal Lie groups

Michael Pevzner (2012)

Annales mathématiques Blaise Pascal

This is an extended version of a lecture given by the author at the summer school “Quasimodular forms and applications” held in Besse in June 2010.The main purpose of this work is to present Rankin-Cohen brackets through the theory of unitary representations of conformal Lie groups and explain recent results on their analogues for Lie groups of higher rank. Various identities verified by such covariant bi-differential operators will be explained by the associativity of a non-commutative product...

Reflexivity of Toeplitz operators in multiply connected regions

Wojciech Młocek, Marek Ptak (2016)

Colloquium Mathematicae

Subspaces of Toeplitz operators on the Hardy spaces over a multiply connected region in the complex plane are investigated. A universal covering map of such a region and the group of automorphisms invariant with respect to the covering map connect the Hardy space on this multiply connected region with a certain subspace of the classical Hardy space on the disc. We also present some connections of Toeplitz operators on both spaces from the reflexivity point of view.

Some results on (strong) asymptotic Toeplitzness and Hankelness

Mehdi Nikpour (2019)

Czechoslovak Mathematical Journal

Based on the results in A. Feintuch (1989), this work sheds light upon some interesting properties of strongly asymptotically Toeplitz and Hankel operators, and relations between these two classes of operators. Indeed, among other things, two main results here are (a) vanishing Toeplitz and Hankel operators forms an ideal, and (b) finding the distance of a strongly asymptotically Toeplitz operator from the set of vanishing Toeplitz operators.

Star products and local line bundles

Richard Melrose (2004)

Annales de l’institut Fourier

The notion of a local line bundle on a manifold, classified by 2-cohomology with real coefficients, is introduced. The twisting of pseudodifferential operators by such a line bundle leads to an algebroid with elliptic elements with real-valued index, given by a twisted variant of the Atiyah-Singer index formula. Using ideas of Boutet de Monvel and Guillemin the corresponding twisted Toeplitz algebroid on any compact symplectic manifold is shown to yield the star products...

Subalgebras to a Wiener type algebra of pseudo-differential operators

Joachim Toft (2001)

Annales de l’institut Fourier

We study general continuity properties for an increasing family of Banach spaces S w p of classes for pseudo-differential symbols, where S w = S w was introduced by J. Sjöstrand in 1993. We prove that the operators in Op ( S w p ) are Schatten-von Neumann operators of order p on L 2 . We prove also that Op ( S w p ) Op ( S w r ) Op ( S w r ) and S w p · S w q S w r , provided 1 / p + 1 / q = 1 / r . If instead 1 / p + 1 / q = 1 + 1 / r , then S w p w * S w q S w r . By modifying the definition of the S w p -spaces, one also obtains symbol classes related to the S ( m , g ) spaces.

Currently displaying 1 – 20 of 21

Page 1 Next