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Minimal projections with respect to various norms

Asuman Güven Aksoy, Grzegorz Lewicki (2012)

Studia Mathematica

A theorem of Rudin permits us to determine minimal projections not only with respect to the operator norm but with respect to various norms on operator ideals and with respect to numerical radius. We prove a general result about N-minimal projections where N is a convex and lower semicontinuous (with respect to the strong operator topology) function and give specific examples for the cases of norms or seminorms of p-summing, p-integral and p-nuclear operator ideals.

Mixed norm condition numbers for the univariate Bernstein basis

Tom Lyche, Karl Scherer (2006)

Banach Center Publications

We study mixed norm condition numbers for the univariate Bernstein basis for polynomials of degree n, that is, we measure the stability of the coefficients of the basis in the l q -sequence norm whereas the polynomials to be represented are measured in the L p -function norm. The resulting condition numbers differ from earlier results obtained for p = q.

Moduli of smoothness of functions and their derivatives

Z. Ditzian, S. Tikhonov (2007)

Studia Mathematica

Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for L p ( T ) and L p [ - 1 , 1 ] for 0 < p < ∞ using the moduli of smoothness ω r ( f , t ) p and ω φ r ( f , t ) p respectively.

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