Entropy numbers, s-numbers, and eigenvalue problems. (English) Zbl 0466.41008


41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
41A35 Approximation by operators (in particular, by integral operators)
42A85 Convolution, factorization for one variable harmonic analysis
47A15 Invariant subspaces of linear operators
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[1] Bauhardt, W, Hilbert zahlen von operatoren in banachräumen, Math. nachr., 79, 181-187, (1977) · Zbl 0364.46052
[2] {\scB. Carl}, Inequalities between absolutely (p, q)-summing norms, Studia Math., in press. · Zbl 0468.47012
[3] {\scB. Carl}, Entropy numbers of diagonal operators with an application to eigenvalue problems, J. Approx. Theory, in press.
[4] {\scB. Carl}, Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems, to appear. · Zbl 0508.47041
[5] Carl, B; Pietsche, A, Entropy numbers of operators in Banach spaces, (), 21-33
[6] {\scB. Carl and H. Triebel}, Inequalities between eigenvalues, entropy numbers and related quantities of compact operators in Banach spaces, Math. Ann., in press. · Zbl 0465.47019
[7] Johnson, W.B; König, H; Maurey, B; Retherford, J.R, Eigenvalues of p-summing and lp-type operators in Banach spaces, J. funct. anal., 32, 353-380, (1979) · Zbl 0408.47019
[8] {\scH. König, J. R. Retherford, N. Tomczak-Jaegermann}, On the eigenvalues of (p, 2)-summing operators and constants associated to normed spaces, J. Funct. Anal., in press. · Zbl 0434.47033
[9] Lewis, D.R, Finite dimensional subspaces of Lp, Studia math., 63, 207-212, (1978) · Zbl 0406.46023
[10] Lewis, D.R; Tomczak-Jaegermann, N, Hilbertian and complimented finite dimensional subspaces of Banach lattices and unitary ideals, J. funct. anal., 35, 165-190, (1980) · Zbl 0422.46019
[11] Lorentz, G.G, Approximation of functions, (1966), Academic Press New York/Toronto/London · Zbl 0153.38901
[12] Mitjagin, B.S, Approximative dimension and bases in nuclear spaces, Uspehi mat. nauk, 16, 4, 63-132, (1961), [Russian]
[13] Mitjagin, B.S; Pelczyński, A, Nuclear operators and approximative dimension, (), 366-372
[14] Peetre, J; Sparr, G, Interpolation of normed abelian groups, Ann. mat. pura appl., 42, 217-262, (1972) · Zbl 0237.46039
[15] Pietsch, A, Operator ideals, (1978), Berlin · Zbl 0399.47039
[16] Pietsch, A, Recent progress and open problems in the theory of operator ideals, (), 23-32
[17] Pietsch, A, Weyl numbers and eigenvalues of operators in Banach spaces, Math. ann., 47, 149-168, (1980) · Zbl 0428.47027
[18] {\scA. Pietsch}, Approximation spaces, preprint. · Zbl 0489.47008
[19] Pisier, G, Estimations des distances á un espace euclidien et des constantes de projection des espaces de Banach de dimension finie; d’après H. König et al., (), Expose X · Zbl 0412.46009
[20] Timan, A.F, Approximation theory of functions of real variables, (1960), [Russian] · Zbl 0125.03504
[21] {\scN. Tomczak-Jaegermann}, Computing 2-summing norm with few vectors, to appear. · Zbl 0436.47033
[22] Triebel, H, Interpolationseigenschaften von entropie- und durchmesseridealen kompakter operatoren, Studia math., 34, 89-107, (1970) · Zbl 0189.43702
[23] Zygmund, A, Trigonometric series, (1968), Cambridge
[24] Third Polish-GDR Seminar on Operator Ideals and Geometry of Banach spaces—Open Problems, Math. Nachr., in press.
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