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Stacey Crossed Products Associated to Exel Systems
Springer Science and Business Media LLC - Tập 72 - Trang 537-561 - 2012
There are many different crossed products by an endomorphism of a C*-algebra,
and constructions by Exel and Stacey have proved particularly useful. Here we
consider Exel crossed products associated to transfer operators which extend to
be unital on the multiplier algebra. We show that every Exel crossed product is
isomorphic to a Stacey crossed product, though by a different endomorphism of a
diff...
On the Properties of Quasi-periodic Boundary Integral Operators for the Helmholtz Equation
Springer Science and Business Media LLC - - 2020
We study the mapping properties of boundary integral operators arising when
solving two-dimensional, time-harmonic waves scattered by periodic domains. For
domains assumed to be at least Lipschitz regular, we propose a novel explicit
representation of Sobolev spaces for quasi-periodic functions that allows for an
analysis analogous to that of Helmholtz scattering by bounded objects. Except
for Ray...
On The Structure of A Commutative Banach Algebra Generated By Toeplitz Operators With Quasi-Radial Quasi-Homogeneous Symbols
Springer Science and Business Media LLC - Tập 74 Số 2 - Trang 199-231 - 2012
Litte Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball
Springer Science and Business Media LLC - Tập 93 - Trang 1-46 - 2021
In this paper, we study the boundedness and the compactness of the little Hankel
operators $$h_b$$ with operator-valued symbols b between different weighted
vector-valued Bergman spaces on the open unit ball $$\mathbb {B}_n$$ in
$$\mathbb {C}^n.$$ More precisely, given two complex Banach spaces X, Y, and
$$0 < p,q \le 1,$$ we characterize those operator-valued symbols $$b: \mathbb
{B}_{n}\rightar...
The strongly irreducible operators in nest algebras
Springer Science and Business Media LLC - Tập 28 - Trang 28-44 - 1997
An operatorT on $$\mathcal{H}$$ is called strongly irreducible ifT does not
commute with any nontrivial idempotent operator. In this paper, we first show
that each nest algebra τ( $$\mathcal{N}$$ ) has strongly irreducible operators.
Secondly, we obtain a characterization of operators which can be uniquely
written as a direct sum of finitely many strongly irreducible operators.
Finally, we charact...
Stability Theorems for Linear Combinations of Idempotents
Springer Science and Business Media LLC - Tập 58 - Trang 597-601 - 2007
We prove a stability theorem for the nullity of a linear combination c 1 P 1 + c
2 P 2 of two idempotent operators P 1, P 2 on a Banach space provided c 1, c 2
and c 1 + c 2 are nonzero. We then show that for c 1 P 1 + c 2 P 2 the property
of being upper semi-Fredholm, lower semi-Fredholm and Fredholm, respectively, is
independent of the choice of c 1, c 2, and that the nullity, defect and index o...
Universal commutative operator algebras and transfer function realizations of polynomials
Springer Science and Business Media LLC - Tập 73 - Trang 305-329 - 2012
To each finite-dimensional operator space E is associated a commutative operator
algebra UC(E), so that E embeds completely isometrically in UC(E) and any
completely contractive map from E to bounded operators on Hilbert space extends
uniquely to a completely contractive homomorphism out of UC(E). The unit ball of
UC(E) is characterized by a Nevanlinna factorization and transfer function
realizati...
Non-selfadjoint periodic Dirac operators with finite-band spectra
Springer Science and Business Media LLC - Tập 36 - Trang 325-348 - 2000
Matrix functions with arbitrarily prescribed left and right partial indices
Springer Science and Business Media LLC - Tập 36 - Trang 71-91 - 2000
We prove that ifn≥2 and ϱ, χ are two given vectors inZ n, then there exists a
matrix function inL ∞ n×n (T) which has a right Wiener-Hopf factorization inL 2
with the partial indices ϱ and a left Wiener-Hopf factorization inL 2 with the
partial indices χ.
Fast state space algorithms for matrix Nehari and Nehari-Takagi interpolation problems
Springer Science and Business Media LLC - Tập 20 - Trang 44-83 - 1994
Numerical algorithms with complexityO(n 2) operations are proposed for solving
matrix Nehari and Nehari-Takagi problems withn interpolation points. The
algorithms are based on explicit formulas for the solutions and on theorems
about cascade decomposition of rational matrix function given in a state space
form. The method suggests also fast algorithms for LDU factorizations of
structured matrices....
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