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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......
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.......
An inverse spectral problem for a nonnormal first order differential operator
Springer Science and Business Media LLC - Tập 25 Số 2 - Trang 147-162 - 1996
Angular cutting for log-hyponormal operators
Springer Science and Business Media LLC - Tập 40 - Trang 383-390 - 2001
We define an angular section for a log-hyponormal operator on a Hilbert space, cut by an arc on the unit circle, and establish various spectral properties for it, which correspond to the properties of an angular section for ap-hyponormal opertor.
Virtual Eigenvalues of the High Order Schrödinger Operator I
Springer Science and Business Media LLC - Tập 55 - Trang 189-231 - 2005
We consider the Schrödinger operator Hγ = ( − Δ)
l
+ γ V(x)· acting in the space
$$L_2 (\mathbb{R}^d ),$$ where 2l ≥ d, V (x) ≥ 0, V (x) is continuous and is not identically zero, and
$$\lim _{|{\mathbf{x}}| \to \infty } V({\mathbf{x}}) = 0.$$ We obtain an asymptotic expansion as
$$\gamma \uparrow 0$$of the bottom negative eigenvalue of Hγ, which is bor......
Nonlinearity inH ∞-control theory, causality in the commutant lifting theorem, and extension of intertwining operators
Springer Science and Business Media LLC - Tập 23 - Trang 89-100 - 1995
The problems studied in this note have been motivated by our work in generalizing linearH
∞ control theory to nonlinear systems. These ideas have led to a design procedure applicable to analytic nonlinear plants. Our technique is a generalization of the linearH
∞ theory. In contrast to previous work on this topic ([9], [10]), we now are able to explicitly incorporate a causality constraint into th......
Weyl’s Theorems for Some Classes of Operators
Springer Science and Business Media LLC - Tập 53 Số 4 - Trang 453-466 - 2005
Irreducibility of Toeplitz C⋆-algebras
Springer Science and Business Media LLC - Tập 9 - Trang 613-622 - 1986
We probe the irreducibility of the Toeplitz C*-algebras generated by Toeplitz operators on Bergman and Hardy spaces associated with generalized upper half-planes in several complex variables.
Nonstationary curves in Hilbert spaces and their correlation functions I
Springer Science and Business Media LLC - - 1994
A Note on the Complete Unitary Invariant for Some Subnormal Operators
Springer Science and Business Media LLC - Tập 77 - Trang 291-298 - 2013
A complete unitary invariant for an irreducible subnormal operators with m.n.e. N satisfying the condition that σ(N) consists of either a Jordan curve or two Jordan curves is given. Also the model of such subnormal operators is established.
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