Series representation of compact linear operators in Banach spaces

• Autorzy: Edmunds D. , Lang J.

Identyfikatory

DOI

10.14708/cm.v56i1.1139

• Języki publikacji: EN

Abstrakty

EN

Let p∈(1,∞) and I=(0,1); suppose that T:L_p(I)→L_p(I) is a~compact linear map with trivial kernel and range dense in L_p(I). It is shown that if the Gelfand numbers of T decay sufficiently quickly, then the action of T is given by a series with calculable coefficients. The special properties of L_p(I) enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.

Słowa kluczowe

EN

eigenvalues; Banach spaces; compact operators; nuclear maps; Gelfand numbers

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: Vol 56, No. 1
• Strony: 17--27
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Edmunds D.

• Department of Mathematics University of Sussex, Pevensey I, Brighton, BNI 9QH, United Kingdom

autor

Lang J.

• Department of Mathematics, The Ohio State University, 100 Math. Tower, 231 West 18th Avenue, Columbus, OH 43210-1174, USA

Bibliografia

• [1]. D. E. Edmunds and W. D. Evans, Representation of compact linear operators in Banach spaces, Birkhäuser, Basel 2013.
• [2]. D. E. Edmunds and J. Lang, The j-eigenfunctions and s-numbers, Math. Nachr. 283 (2010), 463-477, DOI 10.1002/mana.200910221.
• [3]. D. E. Edmunds and J. Lang, Eigenvalues, embeddings and generalised trigonometric functions, Springer, Berlin 2011, DOI 10.1007/978-3-642-18429-1.
• [4]. D. E. Edmunds and J. Lang, Explicit representation of compact linear operators in Banach spaces via polar sets, Studia Math. 214 (2013), 265-278, DOI 10.4064/sm214-3-5.
• [5]. C. Franchetti, The. norm of the minimal projection onto hyperplanes in L^p[0,1] and the radial constant, Boll. U. M. I. (7) 4-B (1990), 803-821.
• [6]. O. Hanner, On the uniform convexity of L^p and l^p, Arkiv Mat. 3 (1956), 239-244.
• [7]. R. C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265-292.
• [8]. Lindenstrauss, On the modulus of smoothness and divergent series in Banach spaces, Mich. Math. J. 10 (1963), 241-252.
• [9]. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. II. Function spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Berlin-New York 1979.
• [10]. Y. P. Odinec, On a property of reflexive Banach spaces with a transitive norm, Bull. Acad. Pol. Math. 25 1982), 353-357.
• [11]. S. Rolewicz, On minimal projections of the space Lp [0,1] on l-codimensional subspace, Bull. Pol. Acad. Soc. Math. 34 (1986), 151-153.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.