| Title:
|
Upper and lower estimates in Banach sequence spaces (English) |
| Author:
|
Gonzalo, Raquel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
641-653 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Here we study the existence of lower and upper $\ell _p$-estimates of sequences in some Banach sequence spaces. We also compute the sharp $\ell _p$ estimates in their basis. Finally, we give some applications to weak sequential continuity of polynomials. (English) |
| Keyword:
|
estimates |
| Keyword:
|
polynomials |
| MSC:
|
46B10 |
| MSC:
|
46B20 |
| MSC:
|
46B45 |
| MSC:
|
46G20 |
| idZBL:
|
Zbl 0851.46016 |
| idMR:
|
MR1378687 |
| . |
| Date available:
|
2009-01-08T18:20:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118793 |
| . |
| Reference:
|
[1] Alencar R., Aron R., Dineen S.: A reflexive space of holomorphic functions in infinitely many variables.Proc. Amer. Math. Soc. 90 (1984), 407-411. Zbl 0536.46015, MR 0728358 |
| Reference:
|
[2] Altshuler R.M., Dineen S.: Uniform convexity in Lorentz sequence spaces.Israel J. Math. 20 (1975), 260-274. MR 0385517 |
| Reference:
|
[3] Aron R.M., Dineen S.: $Q$-reflexive Banach spaces.preprint. Zbl 0916.46011, MR 1627646 |
| Reference:
|
[4] Aron R., LaCruz M., Ryan R., Tonge A.: The generalized Rademacher functions.Note di Math. 22 (1992), 15-25. Zbl 0844.46002, MR 1258560 |
| Reference:
|
[5] Castillo J.M.F., Sánchez F.: Weakly $p$-compact, $p$-Banach Saks and superreflexive spaces.to appear in J. Math. Appl. MR 1125690 |
| Reference:
|
[6] Castillo J.M.F., Sánchez F.: Remarks on the basic properties of Tsirelson's space.to appear in Note di Math. |
| Reference:
|
[7] Farmer J.: Polynomial reflexivity in Banach spaces.Israel J. Math. 87 (1994), 257-273. Zbl 0819.46006, MR 1286830 |
| Reference:
|
[8] Farmer J., Johnson W.B.: Polynomial Schur and Polynomial Dunford Pettis properties.Contemporary Math. 144 (1993), 95-105. Zbl 0822.46013, MR 1209450 |
| Reference:
|
[9] Fetter H., Gamboa B.: The James Forest.book in preparation. Zbl 0878.46010 |
| Reference:
|
[10] Gonzalo R., Jaramillo J.A.: Compact polynomials between Banach spaces.Extracta Math. 8 (1993), 42-48. Zbl 1016.46503, MR 1270328 |
| Reference:
|
[11] Gonzalo R., Jaramillo J.A.: Smoothness and estimates in Banach spaces.Israel J. Math. 89 (1995), 321-341. MR 1324468 |
| Reference:
|
[12] James R.: Superreflexive spaces with basis.Pacific J. Math. 41 (1972), 409-420. MR 0308752 |
| Reference:
|
[13] Jaramillo J.A., Prieto A.: On the weak polynomial convergence on a Banach space.Proc. Amer. Math. Soc. 118 (1993), 463-468. MR 1126196 |
| Reference:
|
[14] Jaramillo J.A., Prieto A., Zalduendo I.: The bidual of the space of polynomials on a Banach space.preprint. Zbl 0901.46030 |
| Reference:
|
[15] Johnson W.B., Odell E.: Subspaces of $L_p$ which embed into $\ell _p$.Compositio Math. 28 (1974), 37-49. MR 0352938 |
| Reference:
|
[16] Knaust H.: Orlicz sequence spaces of Banach Saks type.Archiv Math. 59 (1992), 562-565. Zbl 0735.46009, MR 1189874 |
| Reference:
|
[17] Knaust H., Odell E.: On $c_0$-sequences in Banach spaces.Israel J. Math. 67:2 (1989), 153-169. MR 1026560 |
| Reference:
|
[18] Knaust H., Odell E.: Weakly null sequences with upper $\ell _p$-estimates.(Longhorn Notes) Lecture Notes in Math. 1470, Springer-Verlag, pp. 85-107. MR 1126741 |
| Reference:
|
[19] Lohman R.H., Casazza P.G.: A general construction of spaces of the type of R.C.James.Can. J. Math. 27:6 (1975), 1263-1270. Zbl 0314.46017, MR 0399817 |
| Reference:
|
[20] Lindenstrauss J., Tzafriri L.: Classical Banach Spaces I, II.Springer-Verlag, 1977, 1979. MR 0500056 |
| Reference:
|
[21] Maleev R.P., Troyanski S.L.: Smooth functions in Orlicz spaces.Contemp. Math. 85 (1989), 355-370. Zbl 0691.46010, MR 0983394 |
| Reference:
|
[22] Pelczynski A.: A property of multilinear operations.Studia Math. 16 (1957-58), 173-182. Zbl 0080.09701, MR 0093698 |
| Reference:
|
[23] Ryan R.: Applications of topological tensor spaces to infinite dimensional holomorphy.Ph.D. Thesis, University College, Dublin, 1980. |
| Reference:
|
[24] Sánchez F.: Suceciones débilmente $p$-sumables en espacios de Banach.Tesis doctoral Universidad de Extremadura, 1991. MR 1163592 |
| Reference:
|
[25] Zalduendo I.: An estimate for multilinear forms on $\ell _p$-spaces.to appear in Proc. Royal Irish Acad. 93A/1 (1993), 137-142. MR 1241848 |
| . |
