Comparing gaussian and Rademacher cotype for operators on the space of continuous functions
Junge, Marius
Studia Mathematica, Tome 119 (1996), p. 101-115 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We prove an abstract comparison principle which translates gaussian cotype into Rademacher cotype conditions and vice versa. More precisely, let 2 < q < ∞ and T: C(K) → F a continuous linear operator. (1) T is of gaussian cotype q if and only if (∑k((∥Txk∥F)/(√log(k+1)))q)1/q≤c∥∑kɛkxk∥L2(C(K)), for all sequences (xk)k∈ℕ⊂C(K) with (∥Txk∥)k=1n decreasing. (2) T is of Rademacher cotype q if and only if (∑k(∥Txk∥F√((log(k+1))q))1/q≤c∥∑kgkxk∥L2(C(K)), for all sequences (xk)k∈ℕ⊂C(K) with (∥Txk∥)k=1n decreasing. Our method allows a restriction to a fixed number of vectors and complements the corresponding results of Talagrand.

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:216266 
@article{bwmeta1.element.bwnjournal-article-smv118i2p101bwm,
     author = {Marius Junge},
     title = {Comparing gaussian and Rademacher cotype for operators on the space of continuous functions},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {101-115},
     zbl = {0851.47022},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i2p101bwm}
}

Junge, Marius. Comparing gaussian and Rademacher cotype for operators on the space of continuous functions. Studia Mathematica, Tome 119 (1996) pp. 101-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i2p101bwm/

[00000] [COB] F. Cobos, On the Lorentz-Marcinkiewicz operator ideal, Math. Nachr. 126 (1986), 281-300. | Zbl 0611.47036

[00001] [DJ] M. Defant and M. Junge, On absolutely summing operators with application to the (p,q)-summing norm with few vectors, J. Funct. Anal. 103 (1992), 62-73. | Zbl 0749.47008

[00002] [DJ1] M. Defant and M. Junge, Random variables in weak type p spaces, Arch. Math. (Basel) 58 (1992), 399-406. | Zbl 0764.46010

[00003] [LET] M. Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, 1991. | Zbl 0748.60004

[00004] [LIP] W. Linde and A. Pietsch, Mappings of gaussian cylindrical measures in Banach spaces, Theory Probab. Appl. 19 (1974), 445-460. | Zbl 0312.60005

[00005] [LTI] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, 1977. | Zbl 0362.46013

[00006] [LTII] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer, 1979. | Zbl 0403.46022

[00007] [MAS] V. Mascioni, On weak cotype and weak type in Banach spaces, Note Mat. 8 (1) (1988), 67-110. | Zbl 0818.46020

[00008] [MAU] B. Maurey, Type et cotype dans les espaces munis d'une structure localement inconditionnelle, Sém. Maurey-Schwartz 73-74, École Polytechnique, exp. no. 24-25.

[00009] [MSM] S. J. Montgomery-Smith, The Gaussian cotype of operators from C(K), Israel J. Math. 68 (1989), 123-128. | Zbl 0701.47006

[00010] [PIE] A. Pietsch, Eigenvalues and s-Numbers of Operators, Cambridge Univ. Press, 1987.

[00011] [TAL] M. Talagrand, Cotype of operators from C(K), Invent. Math. 107 (1992), 1-40. | Zbl 0788.47022

[00012] [TA1] M. Talagrand, Regularity of Gaussian processes, Acta Math. 159 (1987), 99-149. | Zbl 0712.60044

[00013] [TJM] N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Longman, 1988.