Pietsch, Albrecht Approximation spaces. (English) Zbl 0489.47008 J. Approximation Theory 32, 115-134 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 54 Documents MSC: 47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) 46A45 Sequence spaces (including Köthe sequence spaces) 47L10 Algebras of operators on Banach spaces and other topological linear spaces 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 47A10 Spectrum, resolvent Keywords:quasi-Banach space; quasi-norm; approximation scheme; approximation numbers; approximation space; Besov spaces; real interpolation scale PDFBibTeX XMLCite \textit{A. Pietsch}, J. Approx. Theory 32, 115--134 (1981; Zbl 0489.47008) Full Text: DOI References: [1] Amanov, T. I., Representation and embedding theorems for functional spaces (Russian), Trudy Mat. Inst. Steklov., 77, 5-34 (1965) [2] Bergh, J.; Löfström, J., Interpolation Spaces (1976), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York · Zbl 0344.46071 [3] Besov, O. V., Investigation of a family of functional spaces in connection with embedding and extension theorems (Russian), Trudy Mat. Inst. Steklov., 60, 42-81 (1961) · Zbl 0116.31701 [4] Brudnij, Ju. A., Approximation spaces (Russian), (Collection of papers on “Geometry of linear spaces and operator theory,” (1977)), 3-30, Jaroslavl [5] Brudnij, Ju. A.; Krugljak, N. Ja., About a family of approximation spaces (Russian), (Collection of papers on “Theory of functions of several real variables,” (1978)), 15-42, Jaroslavl [6] Butzer, P. L.; Scherer, K., Approximationsprozesse und Interpolationsmethoden (1968), Mannheim: Mannheim Zürich · Zbl 0177.08501 [7] Carl, B., Inequalities between absolutely (p, q) -summing norms, Studia Math., 69, 143-148 (1980) · Zbl 0468.47012 [8] Johnson, W. B.; König, H.; Maurey, B.; Retherford, J. R., Eigenvalues of \(p\)-summing and \(l_p\)-type operators in Banach spaces, J. Functional Anal., 32, 353-380 (1979) · Zbl 0408.47019 [9] König, H., \(s\)-Zahlen und Eigenwertverteilungen von Operatoren in Banachräumen, Habilitationsschrift (1977), Bonn [10] König, H., Weyl-type inequalities for operators in Banach spaces, (Proc. Paderborn Conf. Functional Analysis (1979) (1980), North-Holland: North-Holland Amsterdam), 297-317 [11] Lewis, D. R., Finite dimensional subspaces of \(L_p\), Studia Math., 63, 207-212 (1978) · Zbl 0406.46023 [12] Nessel, R. J.; Wilmes, G., Nikolskii-type inequalities for trigonometric polynomials and entire functions of exponential type, J. Austral. Math. Soc. Ser. A, 25, 7-18 (1978) · Zbl 0376.42001 [13] Nikolskij, M. S., Approximation of functions of several variables and embedding theorems (Russian) (1969), Moscow [14] Peetre, J.; Sparr, G., Interpolation of normed abelian groups, Ann. Mat. Pura Appl., 92, 217-262 (1972) · Zbl 0237.46039 [15] Pietsch, A., Operator Ideals (1980), North-Holland: North-Holland Amsterdam · Zbl 0399.47039 [16] Pietsch, A., Einige neue Klassen von kompakten linearen Abbildungen, Rev. Roumaine Math. Pures Appl., 8, 427-447 (1963) · Zbl 0133.07203 [17] Pietsch, A., Factorization theorems for some scales of operator ideals, Math. Nachr., 97, 15-19 (1980) · Zbl 0455.47032 [18] Pietsch, A., Über die Verteilung von Fourierkoeffizienten und Eigenwerten, Wiss. Z. Univ. Jena, 29, 203-211 (1980) · Zbl 0435.47028 [19] Pietsch, A., Eigenvalues of integral operators I, Math. Ann., 247, 169-178 (1980) · Zbl 0428.47028 [20] Stečkin, S. B., About the absolute convergence of orthogonal series (Russian), Dokl. Akad. Nauk SSSR, 102, 37-40 (1955) [21] Triebel, H., Interpolation Theory, Function Spaces, Differential Operators (1978), North-Holland: North-Holland Amsterdam · Zbl 0387.46032 [22] Vogt, D., Integrationstheorie in \(p\)-normierten Räumen, Math. Ann., 173, 219-232 (1967) · Zbl 0159.42601 [23] Zygmund, A., (Trigonometric series (1968), Cambridge Univ. Press: Cambridge Univ. Press London) · JFM 58.0280.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.