Transactions of the American Mathematical Society

Author(s): Patrick N. Dowling; Zhibao Hu; Douglas Mupasiri
Journal: Trans. Amer. Math. Soc. 348 (1996), 127-139.
MSC (1991): Primary 28A05, 46E40
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Abstract: Complex geometric properties of continuously quasi-normed
spaces are introduced and their relationship to their analogues in real Banach spaces is discussed. It is shown that these properties lift from a continuously quasi-normed space $X$

to $L^p(\mu , X)$ , for $0 < p < \infty$ . Local versions of these properties and results are also considered.

1: W.J. Davis, D.J.H. Garling and N. Tomczak-Jaegermann, The complex convexity of quasi-normed spaces, J. Funct. Anal. 55 (1984), 110-150, MR 86b:46032.
2: S.J. Dilworth, Complex convexity and the geometry of Banach spaces, Math. Proc. Camb. Phil. Soc. 99 (1986), 495-506, MR 87k:46032.
3: P.N. Dowling, Z. Hu and M.A. Smith, Geometry of spaces of vector-valued harmonic functions, Can. J. Math. 46(2) (1994), 274-283, MR 95b:46054.
4: P. Greim, An extremal vector-valued -function taking no extremal vectors as values, Proc. Amer. Math. Soc. 84 (1982), 65-68, MR 83c:46034.
5: P. Greim, A note on strong extreme and strongly exposed points in Bochner -spaces, Proc. Amer. Math. Soc. 93 (1985), 65-66, MR 86g:46050.
6: Z. Hu and D.Mupasiri, Complex strongly extreme points in quasi-normed spaces, preprint (1994).
7: J.A. Johnson, Extreme measurable selections, Proc. Amer. Math. Soc. 44 (1974), 107-112, MR 49:5818.
8: D. Mupasiri, Some results on complex convexity and the geometry of complex vector spaces, Dissertation, Northern Illinois University (1992).
9: M.A. Smith, Strongly extreme points in $L^p(\mu , X)$ , Rocky Mountain J. Math. 16 (1986), 1-5, MR 87d:46043.
10: M.A. Smith, Rotundity and extremity in $\ell ^p(X_i)$ and $L^p(\mu , X)$ , Contemporary Math. 52 (1986), 143-162, MR 87h:46053.
11: M.A. Smith and B. Turett, Rotundity in Lebesgue-Bochner function spaces, Trans. Amer. Math. Soc. 257 (1980), 105-118, MR 80m:46031.
12: K. Sundaresan, Extreme points of the unit cell in Lebesgue-Bochner function spaces. I, Proc. Amer. Math. Soc. 23 (1969), 179-184, MR 40:719.
13: K. Sundaresan, Extreme points of the unit cell in Lebesgue-Bochner function spaces, Colloq. Math. 22 (1970), 111-119, MR 43:2493.
14: E. Thorp and R. Whitley, The strong maximum modulus theorem for analytic functions into a Banach space, Proc. Amer. Math. Soc. 18 (1967), 640-646, MR 35:5643.
15: Q. Xu, Inégalités pour les martingales de Hardy et renormage des espaces quasi-normés, C.R. Acad. Sci. Paris, Sér. I 306 (1988), 601-604, MR 89k:46029.
16: Q. Xu, Convexités uniformes et inégalités de martingales, Math. Ann. 287 (1990), 193-211, MR 91m:46027.

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 28A05, 46E40

Patrick N. Dowling
Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
Email: pndowling@miavx1.acs.muohio.edu

Zhibao Hu
Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
Address at time of publication: Department of Mathematics, El Paso Community College, P.O. Box 20500, Elpaso, Texas 79998
Email: davidhu@laguna.epcc.edu

Douglas Mupasiri
Affiliation: Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa 50614
Email: mupasiri@math.uni.edu

DOI: 10.1090/S0002-9947-96-01508-5
PII: S 0002-9947(96)01508-5
Keywords: Quasi-normed spaces, complex extreme points, complex strongly extreme points, analytic denting points
Received by editor(s): July 22, 1994.
Copyright of article: Copyright 1996, American Mathematical Society

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