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On the Norm of Elementary Operators 总被引:3,自引:0,他引:3
The norm problem is considered for elementary operators of theform Ua,b: AA,x axb+bxa (a,bA) in the special case when A isa subalgebra of the algebra of bounded operators on a Banachspace. In particular, the lower estimate || is established when the Banach space is a Hilbertspace and A is the algebra of all bounded linear operators. 相似文献
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Thomas Ransford 《Set-Valued Analysis》1999,7(2):159-194
We show how the theory of analytic multifunctions can be developed in an elementary and self-contained fashion, using the abstract notions of gauge and multigauge. This approach also yields new information about the metric properties of analytic multifunctions, leading to analogues of Schwarz's lemma and the Schwarz–Pick theorem. 相似文献
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We present an example of a pair of 4×4 matrices having identical pseudospectra but whose squares have different norms. The novelty of the example lies in the fact that the matrices in question have only simple eigenvalues. 相似文献
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Let (an)n0 be a sequence of complex numbers, and, for n0, let
A number of results are proved relating the growth of the sequences(bn) and (cn) to that of (an). For example, given p0, if bn= O(np and for all > 0,then an=0 for all n > p. Also, given 0 < p < 1, then for all > 0 if and onlyif . It is further shown that, given rß > 1, if bn,cn=O(rßn), then an=O(n),where , thereby proving a conjecture of Chalendar, Kellay and Ransford. The principal ingredientsof the proogs are a Phragmén-Lindelöf theorem forentire functions of exponential type zero, and an estimate forthe expected value of e(X), where X is a Poisson random variable.2000 Mathematics Subject Classification 05A10 (primary), 30D15,46H05, 60E15 (secondary). 相似文献
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Javad Mashreghi Julian Ransford Thomas Ransford 《Journal of Functional Analysis》2018,274(11):3254-3262
We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of weighted composition operators on the Dirichlet space as being exactly those linear maps that send nowhere-vanishing functions to nowhere-vanishing functions.We also investigate possible extensions to weighted Dirichlet spaces with superharmonic weights. As part of our investigation, we are led to determine which of these spaces contain functions that map the unit disk onto the whole complex plane. 相似文献
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Let
be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable.
We give a new sufficient condition, not far from the known necessary condition, for a function f∈
to be cyclic, i.e. for {pf: p is a polynomial} to be dense in
.
The proof is based on the notion of Bergman–Smirnov exceptional set introduced by Hedenmalm and Shields. Our methods yield
the first known examples of such sets that are uncountable. One of the principal ingredients of the proof is a new converse
to the strong-type inequality for capacity. 相似文献
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We study the lemniscates of rational maps. We prove a reflection principle for the harmonic measure of rational lemniscates and we give estimates for their capacity and the capacity of their components. Also, we prove a version of Schwarz’s lemma for the capacity of the lemniscates of proper holomorphic functions. 相似文献
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Omar El-Fallah Emmanuel Fricain Karim Kellay Javad Mashreghi Thomas Ransford 《Constructive Approximation》2016,44(2):269-281
In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function f can be approximated in norm by its dilates \(f_r(z):=f(rz)~(r<1)\). We show that this is not the case for the de Branges–Rovnyak spaces \(\mathcal{H}(b)\). More precisely, we exhibit a space \(\mathcal{H}(b)\) in which the polynomials are dense and a function \(f\in \mathcal{H}(b)\) such that \(\lim _{r\rightarrow 1^-}\Vert f_r\Vert _{\mathcal{H}(b)}=\infty \). On the positive side, we prove the following approximation theorem for Toeplitz operators on general de Branges–Rovnyak spaces \(\mathcal{H}(b)\). If \((h_n)\) is a sequence in \(H^\infty \) such that \(\Vert h_n\Vert _{H^\infty }\le 1\) and \(h_n(0)\rightarrow 1\), then \(\Vert T_{\overline{h}_n}f-f\Vert _{\mathcal{H}(b)}\rightarrow 0\) for all \(f\in \mathcal{H}(b)\). Using this result, we give the first constructive proof that, if b is a nonextreme point of the unit ball of \(H^\infty \), then the polynomials are dense in \(\mathcal{H}(b)\). 相似文献