Notes on binary trees of elements in C(K) spaces with an application to a proof of a theorem of H. P. Rosenthal

• Autorzy: Michalak A.
• Języki publikacji: EN

Abstrakty

EN

A Banach space X contains an isomorphic copy of C([0, 1]), if it contains a binary tree (en) with the following properties (1) e_n = e_2n + e_2n+1 and (2) [formuła]. We present a proof of the following generalization of a Rosenthal result: if E is a closed subspace of a separable C(K) space with separable annihilator and S : E - X is a continuous linear operator such that S* has nonseparable range, then there exists a subspace Y of E isomorphic to C([0, 1]) such that S|Y is an isomorphism, based on the fact.

Słowa kluczowe

EN

C(K)-spaces

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2006
• Tom: Vol. 46, [Z] 2
• Strony: 233--244
• Opis fizyczny: bibliogr. 15 poz.

Twórcy

autor

Michalak A.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University ul. Umultowska 87, 61-614 Poznań, Poland,

Bibliografia

• [1] C. D. Aliprantis and O. Burkinshaw, Positive operators, Academic Press Inc. 1985.
• [2] D. E. Alspach, C(α) preserving operators on separable Banach spaces, J. Funct. Anal. 45 (1982), 139-168.
• [3] J. Diestel, Sequences and Series in Banach Spaces, Graduate Texts in Mathematics, 92, Springer-Verlag 1984.
• [4] M. Engelking, General Topology, Monografie Matematyczne 60, PWN - Polish Scientific Publishers, Warszawa 1977.
• [5] T. Gamelin, Uniform algebras, Prentice-Hall, INC., Englewood Cliffs, N.J. 1969.
• [6] H. P. Lotz and H. P. Rosenthal, Embeddings of C(Δ) and L1[0, 1] in Banach lattices, Israel J. Math. 31 (1978), 169-179.
• [7] A. Michalak, On monotonic functions from the unit interval into a Banach spaces with uncountable set of points of discontinuity, Studia Math. 155 (2003), 171-182.
• [8] A. Michalak, On continuous linear operators on D[0, 1) with nonseparable ranges, Commentationes Math. 43 (2003), 221-248.
• [9] A. Pełczyński, Banach spaces of analytic functions and absolutely summing operators, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No.30., AMS, Providence, R.I. 1977.
• [10] H. P. Rosenthal, On factors of C([0, 1]) with nonseparable dual, Israel J. Math. 13 (1973), 361-378.
• [11] H. P. Rosenthal, Correction to: "On factors of C([0, 1]) with nonseparable dual" Israel J. Math. 21 (1975), 93-94.
• [12] H. P. Rosenthal, The Banach spaces C(K), Handbook of the Geometry of Banach Spaces, Vol.2 ed. W. B. Johnson and J. Lindenstrauss, Elsevier Science B.V., Amsterdam, 2003, 1547-1602.
• [13] W. Rudin, Real and Complex Analysis, Mc Graw-Hill, Inc. 1974.
• [14] P. Wojtaszczyk, Banach Spaces for Analysts, Cambridge University Press, Cambridge 1991.
• [15] L. W. Weis, The range of an operator in C(X) and its representing stochastic kernel, Arch. Math. 46 (1986), 171-178.