Analytic families of operators on some quasi-Banach spaces

Authors:
Michael Cwikel and Yoram Sagher

Journal:
Proc. Amer. Math. Soc. **102** (1988), 979-984

MSC:
Primary 46M35; Secondary 42B30, 46E10

MathSciNet review:
934878

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An interpolation theorem for analytic families of operators on some quasi-Banach spaces is proved. The result is applicable to spaces whose quasi-norm is defined by means of a maximal function, for example the various spaces on locally compact groups.

**[1]**A.-P. Calderón,*Intermediate spaces and interpolation, the complex method*, Studia Math.**24**(1964), 113–190. MR**0167830****[2]**R. R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher, and G. Weiss,*A theory of complex interpolation for families of Banach spaces*, Adv. in Math.**43**(1982), no. 3, 203–229. MR**648799**, 10.1016/0001-8708(82)90034-2**[3]**Michael Cwikel and Svante Janson,*Interpolation of analytic families of operators*, Studia Math.**79**(1984), no. 1, 61–71. MR**772005****[4]**M. Cwikel, M. Milman, and Y. Sagher,*Complex interpolation of some quasi-Banach spaces*, J. Funct. Anal.**65**(1986), no. 3, 339–347. MR**826431**, 10.1016/0022-1236(86)90023-6**[5]**I. I. Hirschman Jr.,*A convexity theorem for certain groups of transformations*, J. Analyse Math.**2**(1953), 209–218. MR**0057936****[6]**N. J. Kalton,*Convexity conditions for nonlocally convex lattices*, Glasgow Math. J.**25**(1984), no. 2, 141–152. MR**752808**, 10.1017/S0017089500005553**[7]**N. J. Kalton,*Plurisubharmonic functions on quasi-Banach spaces*, Studia Math.**84**(1986), no. 3, 297–324. MR**877084****[8]**Yoram Sagher,*On analytic families of operators*, Israel J. Math.**7**(1969), 350–356. MR**0257822****[9]**-,*Interpolation of some analytic families of operators*, Proc. U.S. Swedish Seminar on Function Spaces and Applications, Lecture Notes in Math., vol. 1302, Springer.**[10]**Elias M. Stein,*Interpolation of linear operators*, Trans. Amer. Math. Soc.**83**(1956), 482–492. MR**0082586**, 10.1090/S0002-9947-1956-0082586-0

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
46M35,
42B30,
46E10

Retrieve articles in all journals with MSC: 46M35, 42B30, 46E10

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1988-0934878-4

Article copyright:
© Copyright 1988
American Mathematical Society