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1.
Aleksej Turnšek 《Monatshefte für Mathematik》2001,132(4):349-354
Let denote the von Neumann–Schatten class, its norm and let be an elementary operator defined by . We shall characterize those operators which are orthogonal to the range of in the sense that for all . The main results of this paper are: If and (i) if A, C, respectively B, D are commuting normal operators with , or (ii) if A, B are contractions and , then is orthogonal to the range of if and only of S is in the kernel of . Furthermore, in both cases, the algebraic direct sum satisfies .
(Received 9 February 2000; in revised form 21 February, 2001) 相似文献
2.
In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ. 相似文献
3.
T. Len Miller Vivien G. Miller Michael M. Neumann 《Mediterranean Journal of Mathematics》2009,6(2):149-168
This paper centers on local spectral conditions that are both necessary and sufficient for the equality of the essential spectra
of two bounded linear operators on complex Banach spaces that are intertwined by a pair of bounded linear mappings. In particular,
if the operators T and S are intertwined by a pair of injective operators, then S is Fredholm provided that T is Fredholm and S has property (δ) in a neighborhood of 0. In this case, ind(T) ≤ ind(S), and equality holds precisely when the eigenvalues of the adjoint T* do not cluster at 0. By duality, we obtain refinements of results due to Putinar, Takahashi, and Yang concerning operators
with Bishop’s property (β) intertwined by pairs of operators with dense range. Moreover, we establish an extension of a result due to Eschmeier that,
under appropriate assumptions regarding the single-valued extension property, leads to necessary and sufficient conditions
for quasi-similar operators to have equal essential spectra. In particular it turns out that the single-valued extension property
plays an essential role in the preservation of the index in this context.
相似文献
4.
5.
Alexey I. Popov 《Integral Equations and Operator Theory》2010,67(2):247-256
Given a Banach space X and a bounded linear operator T on X, a subspace Y of X is almost invariant under T if TY í Y+F{TY\subseteq Y+F} for some finite-dimensional “error” F. In this paper, we study subspaces that are almost invariant under every operator in an algebra
\mathfrak A{\mathfrak A} of operators acting on X. We show that if
\mathfrak A{\mathfrak A} is norm closed then the dimensions of “errors” corresponding to operators in
\mathfrak A{\mathfrak A} must be uniformly bounded. Also, if
\mathfrak A{\mathfrak A} is generated by a finite number of commuting operators and has an almost invariant half-space (that is, a subspace with both
infinite dimension and infinite codimension) then
\mathfrak A{\mathfrak A} has an invariant half-space. 相似文献
6.
A bijective linear mapping between two JB-algebrasA andB is an isometry if and only if it commutes with the Jordan triple products ofA andB. Other algebraic characterizations of isometries between JB-algebras are given. Derivations on a JB-algebraA are those bounded linear operators onA with zero numerical range. For JB-algebras of selfadjoint operators we have: IfH andK are left Hilbert spaces of dimension ≥3 over the same fieldF (the real, complex, or quaternion numbers), then every surjective real linear isometryf fromS(H) ontoS(K) is of the formf(x)=UoxoU
−1 forx inS(H), whereτ is a real-linear automorphism ofF andU is a real linear isometry fromH ontoK withU(λh)=τ(λ)U(h) for λ inF andh inH.
Supported by Acción Integrada Hispano-Alemana HA 94 066 B 相似文献
7.
A Banach space X has the alternative Dunford–Pettis property if for every weakly convergent sequences (xn) → x in X and (xn*) → 0 in X* with ||xn|| = ||x||= 1 we have (xn*(xn)) → 0. We get a characterization of certain operator spaces having the alternative Dunford–Pettis property. As a consequence
of this result, if H is a Hilbert space we show that a closed subspace M of the compact operators on H has the alternative Dunford–Pettis property if, and only if, for any h ∈ H, the evaluation operators from M to H given by S ↦ Sh, S ↦ Sth are DP1 operators, that is, they apply weakly convergent sequences in the unit sphere whose limits are also in the unit sphere
into norm convergent sequences. We also prove a characterization of certain closed subalgebras of K(H) having the alternative Dunford-Pettis property by assuming that the multiplication operators are DP1. 相似文献
8.
Yang Changsen Li Haiying 《高校应用数学学报(英文版)》2006,21(1):64-68
The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal. 相似文献
9.
Dumitru Popa 《Proceedings Mathematical Sciences》2009,119(2):221-230
Let Ω be a compact Hausdorff space, X a Banach space, C(Ω, X) the Banach space of continuous X-valued functions on Ω under the uniform norm, U: C(Ω, X) → Y a bounded linear operator and U
#, U
# two natural operators associated to U. For each 1 ≤ s < ∞, let the conditions (α) U ∈ Π
s
(C(Ω, X), Y); (β)U
# ∈ Π
s
(C(Ω), Π
s
(X, Y)); (γ) U
# ε Π
s
(X, Π
s
(C(Ω), Y)). A general result, [10, 13], asserts that (α) implies (β) and (γ). In this paper, in case s = 2, we give necessary and sufficient conditions that natural operators on C([0, 1], l
p
) with values in l
1 satisfies (α), (β) and (γ), which show that the above implication is the best possible result. 相似文献
10.
In this paper we consider operators acting on a subspace ℳ of the space L
2 (ℝm; ℂm) of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace
ℳ is defined as the orthogonal sum of spaces ℳs,k of specific Clifford basis functions of L
2(ℝm; ℂm).
Every Clifford endomorphism of ℳ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic
operators are characterized in terms of commutation relations and they transform a space ℳs,k into a similar space ℳs′,k′. Hence, once the Clifford-Hermite-monogenic decomposition of an operator is obtained, its action on the space ℳ is known.
Furthermore, the monogenic decomposition of some important Clifford differential operators with polynomial coefficients is
studied in detail. 相似文献
11.
Hua-Ping Yu 《代数通讯》2013,41(6):2187-2197
An associative ring R with identity is said to have stable range one if for any a,b? R with aR + bR = R, there exists y ? R such that a + by is left (equivalently, right) invertible. The main results of this note are Theorem 2: A left or right continuous ring R has stable range one if and only if R is directly finite (i.e xy = 1 implies yx = 1 for all x,y ? R), Theorem 6: A left or right N 0o-quasi-continuous exchange ring has stable range one if and only if it is directly finite, and Theorem 12: left or right N 0-quasi-continuous strongly π-regular rings have stable range one. Theorem 6 generalizes a well-known result of Goodearl [10], which says that a directly finite, right N o-continuous von Neumann regular ring is unit-regular 相似文献
12.
13.
Stein’s higher Riesz transforms are translation invariant operators on L
2(R
n
) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this
article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete
series representations for hyperboloids associated to the indefinite quadratic form of signature (p,q). We prove that these operators extend to L
r
-bounded operators for 1<r<∞ if the parameter of the discrete series representations is generic. 相似文献
14.
Let −A be a linear, injective operator, on a Banach spaceX. We show that ∃ anH
∞ functional calculus forA if and only if −A generates a bouned strongly continuous holomorphic semigroup of uniform weak bounded variation, if and only ifA(ζ+A)
−1 is of uniform weak bounded variation. This provides a sufficient condition for the imaginary powers ofA, {A−is} sεR, to extend to a strongly continuous group of bounded operators; we also give similar necessary conditions. 相似文献
15.
K. Varadarajan 《Proceedings Mathematical Sciences》1999,109(4):345-351
Define a ringA to be RRF (resp. LRF) if every right (resp. left) A-module is residually finite. Refer to A as an RF ring if it is simultaneously
RRF and LRF. The present paper is devoted to the study of the structure of RRF (resp. LRF) rings. We show that all finite
rings are RF. IfA is semiprimary, we show thatA is RRF ⇔A is finite ⇔A is LRF. We prove that being RRF (resp. LRF) is a Morita invariant property. All boolean rings are RF. There are other infinite
strongly regular rings which are RF. IfA/J(A) is of bounded index andA does not contain any infinite family of orthogonal idempotents we prove:
IfA is one sided quasi-duo (left or right immaterial) not containing any infinite family of orthogonal idempotents then (i) and
(ii) are valid with the further strengthening thatA/J(A) is a finite product of finite fields. 相似文献
(i) | A an RRF ring ⇔ A right perfect andA/J(A) finite (henceA/J(A) finite semisimple artinian). |
(ii) | A an LRF ring ⇔ A left perfect andA/J(A) finite |
16.
The ℒ
p
spaces which were introduced by A. Pełczyński and the first named author are studied. It is proved, e.g., that (i)X is an ℒ
p
space if and only ifX* is and ℒ
q
space (p
−1+q
−1=1). (ii) A complemented subspace of an ℒ
p
space is either an ℒ
p
or an ℒ2 space. (iii) The ℒ
p
spaces have sufficiently many Boolean algebras of projections. These results are applied to show thatX is an ℒ∞ (resp. ℒ1) space if and only ifX admits extensions (resp. liftings) of compact operators havingX as a domain or range space. We also prove a theorem on the “local reflexivity” of an arbitrary Banach space.
This research was partially supported by NSF Grant# 8964. 相似文献
17.
We study self adjoint operators of the form?H
ω = H
0 + ∑λω(n) <δ
n
,·>δ
n
,?where the δ
n
’s are a family of orthonormal vectors and the λω(n)’s are independently distributed random variables with absolutely continuous probability distributions. We prove a general
structural theorem saying that for each pair (n,m), if the cyclic subspaces corresponding to the vectors δ
n
and δ
m
are not completely orthogonal, then the restrictions of H
ω to these subspaces are unitarily equivalent (with probability one). This has some consequences for the spectral theory of
such operators. In particular, we show that “well behaved” absolutely continuous spectrum of Anderson type Hamiltonians must
be pure, and use this to prove the purity of absolutely continuous spectrum in some concrete cases.
Oblatum 27-V-1999 & 6-I-2000?Published online: 8 May 2000 相似文献
18.
If a and b are trace-class operators, and if u is a partial isometry, then , where ∥⋅∥1 denotes the norm in the trace class. The present paper characterises the cases of equality in this Young inequality, and
the characterisation is examined in the context of both the operator and the Hilbert–Schmidt forms of Young's inequality.
Received: 20 December 2001 / Revised version: 11 July 2002 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 47A63, 15A60 相似文献
19.
Certain convolution operators of the form (K f) (t) = A∈t
0
t
L(t-s) f(s) ds , where A is the infinitesimal generator of either a C
0
-group or a C
0
-cosine family in a Banach space E , are considered. We obtain several lifting results guaranteeing that the continuity of K from L
p
to L
q
implies the continuity of K from L
p
to L
∈
fty . These results are applied to the study of multiplicative perturbations of C
0
-groups and C
0
-cosine families in Banach spaces and to the study of the Maximal Regularly Property (MRP) in L
p
, 1 ≤ p ≤ +∈fty , for second-order Cauchy problem. It is proved that the MRP is equivalent to the boundedness of the infinitesimal generator.
April 30, 1999 相似文献
20.
We consider singular integral operators of the form (a)Z
1L−1Z2, (b)Z
1Z2L−1, and (c)L
−1Z1Z2, whereZ
1 andZ
2 are nonzero right-invariant vector fields, andL is theL
2-closure of a canonical Laplacian. The operators (a) are shown to be bounded onL
p for allp∈(1, ∞) and of weak type (1, 1), whereas all of the operators in (b) and (c) are not of weak type (p, p) for anyp∈[1, ∞).
Research supported by the Australian Research Council.
Research carried out as a National Research Fellow. 相似文献