Results 251 to 260 of about 770,686 (284)

Norms and Essential Norms of Differences of Weighted Composition Operators

Mediterranean Journal of Mathematics, 2022
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Operator Norm Limits of Order Continuous Operators

Positivity, 2005
Let \(X\) and \(Y\) be Banach lattices, and denote by \({\mathcal L}^b(X, Y)\) the space of order bounded linear operators from \(X\) into \(Y\) equipped with the order bound norm, a norm introduced by the second author [in: Functional analysis and economic theory, Samos, Greece, July 1996, 109--118 (1998; Zbl 0912.47018)]. Moreover, let \({\mathcal L}^
Wickstead, Anthony, Kitover, A.K.
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Norm Estimates for Commutators of Operators

Journal of the London Mathematical Society, 1998
Suppose \(A\), \(B\) are two selfadjoint operators and \(f(x)\) is a continuous function on some interval containing their spectra. In case \(f'\) is bounded, one would expect to find an estimate of the form \[ \| f(A)- f(B) \|\leq \text{const} \| f' \|_\infty \| A-B \|. \] However, this is not true in general (a counterexample was given, for instance,
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The Essential Norm of a Composition Operator

The Annals of Mathematics, 1987
Let \(\Omega\subset{\mathbb{C}}^ n\) be a domain and \(\Phi: \Omega\to \Omega\) a mapping. The operator \(T: f\to f\circ \Phi\) is called a composition operator. The subject of composition operators represents a fertile arena for the interaction of operator theory, hard analysis, and geometry.
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The Norms of Compositions of Arithmetic Operators

Bulletin of the London Mathematical Society, 1987
Weighted inequalities which widely generalize the Turán-Kubilius inequality are established. The following is typical: Let w(m) be a non- negative real-valued arithmetic function which satisfies w(q) \(\ll 1\), w(qm) \(\ll w(q)w(m)\) uniformly for prime-powers q and positive integers m, \((q,m)=1\).
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A Norm Inequality for Hermitian Operators

The American Mathematical Monthly, 2003
(2003). A Norm Inequality for Hermitian Operators. The American Mathematical Monthly: Vol. 110, No. 3, pp. 238-239.
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Some Norm Inequalities for Operators

Canadian Mathematical Bulletin, 1999
AbstractLet Ai , Bi and Xi (i = 1, 2,…,n) be operators on a separable Hilbert space. It is shown that if f and g are nonnegative continuous functions on [0, ∞) which satisfy the relation f(t)g(t) = t for all t in [0, ∞), thenfor every r > 0 and for every unitarily invariant norm. This result improves some known Cauchy-Schwarz type inequalities. Norm
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On probabilistic norm of a linear operators and space of operators

Applied Mathematics and Mechanics, 1999
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Estimates for the Norm of the Hardy Operator in Operator Ideals

Siberian Mathematical Journal
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E. N. Lomakina, M. G. Nasyrova
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Extreme values of operator norms in spaces with equivalent norms

Journal of Mathematical Sciences, 1999
Let \((L,\|\cdot\|)\) and \((L,\|\cdot\|_{\ast})\) be normed spaces and let the norms \(\|\cdot\|\) and \(\|\cdot\|_{\ast}\) be equivalent. Then there exist the exact constants \(\alpha\) and \(\beta\) such that \(\alpha\|\cdot\|\leq\|\cdot\|_{\ast}\leq\beta\|\cdot\|.\) The functional \[ \rho\left(\|\cdot\|,\|\cdot\|_{\ast}\right) =\ln\frac{\beta ...
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