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M. R. Weber 《Mathematische Nachrichten》2009,282(10):1478-1487
In Banach spaces ordered by a normal cone that contains interior points the positive invertibility of operators is studied. If there exists a uniformly positive functional then any positively invertible operator A possesses a B -decomposition, i.e., a positive decomposition A = U – V with the properties: U–1 exists, VU–1 ≥ 0, Ax ≥ 0, U x ≥ 0 imply x ≥ 0 and r (VU–1) < 1. Earlier it was shown that the existence of a B -decomposition with r (VU–1) < 1 is sufficient for the positive invertibility of the operator A. Peris' result is obtained as a special case of the main theorem. The decomposition is demonstrated for a positively invertible operator in a Banach space ordered by an ice cream cone (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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We obtain the conditions of one-valued solvability of some infinite-dimensional pseudodifferential equations and construct some classes of invertible pseudodifferential operators with symbols depending on two arguments.Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 9, Suzdal Conference-3, 2003. 相似文献
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The topologies of simple convergence and of bounded convergence are shown to coincide on the spaces of Hankel multipliers
and of Hankel convolution operators. The properties of these spaces being bornological, nuclear, Montel, and reflexive are
established. 相似文献
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This paper is a continuation of [GK3] where the theory of Invertibility Symbol in Banach algebras was developed. In the present paper we generalize these results for the case when the Invertibility Symbol is defined on a subalgebra of the Banach algebras. The difficulty which arises here in this more general case is connected with the fact that some elements of the subalgebra may have the inverses which do not belong to the subalgebra. This generalization of the theory allows us to study the Fredholm Symbols of linear operators. Applications to subalgebras generated by two idempotents and to algebras generated by singular integral operators are presented. 相似文献
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Toeplitz operators and Hankel operators 总被引:2,自引:0,他引:2
Dechao Zheng 《Integral Equations and Operator Theory》1989,12(2):280-299
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We give an interpolation-free proof of the known fact that a dyadic paraproduct is of Schatten-von Neumann class Sp, if and only if its symbol is in the dyadic Besov space Bpd. Our main tools are a product formula for paraproducts and a “p-John-Nirenberg-Theorem” due to Rochberg and Semmes.We use the same technique to prove a corresponding result for dyadic paraproducts with operator symbols.Using an averaging technique by Petermichl, we retrieve Peller's characterizations of scalar and vector Hankel operators of Schatten-von Neumann class Sp for 1<p<∞. We then employ vector techniques to characterise little Hankel operators of Schatten-von Neumann class, answering a question by Bonami and Peloso.Furthermore, using a bilinear version of our product formula, we obtain characterizations for boundedness, compactness and Schatten class membership of products of dyadic paraproducts. 相似文献
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Vladimir V. Peller 《Integral Equations and Operator Theory》1982,5(1):244-272
The Hankel operators of the class on the spaces of vector-valued functions are characterized in terms of their symbols. Different applications are considered. It is proved that the averaging projection onto the block-Hankel matrices is bounded on for 1 < p < + . A criterion for an operator commuting with a Coo contraction to be in is obtained in terms of the Sz.-Nagy-Foia lifting theorem. Finally the obtained results are applied to describe various commutators of the class. 相似文献
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A new class of pseudodifferential operators with degeneration is considered. The operators are constructed using a special integral transform mapping a weighted differentiation operator to a multiplication operator. The composition and boundedness properties of such operators in special weighted spaces are examined. Theorems on commutation of such operators with differentiation operators are obtained. The behavior of these operators as t → 0and t → +∞ is investigated. The properties of adjoint operators are studied, and an analogue of Gårding’s inequality is proved. 相似文献
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V. I. Ovchinnikov 《Mathematical Notes》1971,10(5):749-753
We prove that for any Fredholm operator A(x) of class C1 and zero index in a Hilbert space, in a neighborhood of any star compactum T lying in the domain of A we can define a completely continuous and continuously differentiable operator C, so that the linear operator A(x)+ C(x) has a bounded inverse for all xT.Translated from Matematicheskie Zametki, Vol. 10, No. 5, pp. 541–548, November, 1971.The author wishes to thank M. A. Krasnosel'skii for posing the problem, and P. P. Zabreiko and S. G. Krein for their interest in this work. 相似文献
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Quanlei Fang 《Journal of Functional Analysis》2009,257(10):3082-673
Let H2(S) be the Hardy space on the unit sphere S in Cn, n?2. Consider the Hankel operator Hf=(1−P)Mf|H2(S), where the symbol function f is allowed to be arbitrary in L2(S,dσ). We show that for p>2n, Hf is in the Schatten class Cp if and only if f−Pf belongs to the Besov space Bp. To be more precise, the “if” part of this statement is easy. The main result of the paper is the “only if” part. We also show that the membership Hf∈C2n implies f−Pf=0, i.e., Hf=0. 相似文献