A note on the imbedding theorem of Browder and Ton

Author:
J. Berkovits

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2963-2966

MSC (2000):
Primary 47H05, 78M99

DOI:
https://doi.org/10.1090/S0002-9939-03-07094-1

Published electronically:
April 9, 2003

MathSciNet review:
1974355

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Abstract | References | Similar Articles | Additional Information

Abstract: The imbedding theorem of Browder and Ton states that for any real separable Banach space there exist a real separable Hilbert space and a compact linear injection such that is dense in We shall give a short and elementary new proof to this result. We also briefly discuss the corresponding result without the completeness assumption.

**1.**R.A. Adams,*Sobolev Spaces*, Academic Press, 1975. MR**56:9247****2.**Y.I. Alber,*The solution of nonlinear equations with monotone operators in a Banach space*, Siberian Math. J. 16 (1) (1975) pp. 1-8. MR**51:6512****3.**H. Amann,*An existence and unicity theorem for the Hammerstein equation in Banach spaces*, Math. Z. 111 (3) (1969) pp. 175-190. MR**40:7894****4.**J. Berkovits,*On the degree theory for nonlinear mappings of monotone type*, Ann. Acad. Sci. Fenn. Ser. A1, Dissertationes, 58 (1986). MR**87f:47084****5.**J. Berkovits and V. Mustonen,*On the topological degree for mappings of monotone type*, Nonlinear Anal., TMA, 10 (1986) pp. 1373-1383. MR**88b:47073****6.**J. Berkovits and M. Tienari,*Topological degree for some classes of multis with applications to hyperbolic and elliptic problems involving dicontinuous nonlinearities*, Dynamic Systems and Applications 5 (1996) pp. 1-18. MR**96m:47112****7.**F.E. Browder and B.A. Ton,*Nonlinear functional equations in Banach spaces and elliptic super-regularization*, Math. Z. 105 (1968) pp. 177-195. MR**38:582****8.**A.A. Khan,*A regularization approach for variational inequalities*, Comput. Math. Appl. 42 (1-2), (2001) pp. 65-74. MR**2002b:49020****9.**D. Pascali and S. Sburlan,*Nonlinear Mappings of Monotone Type*, Editura Academiei, 1978. MR**80g:47056****10.**C.G. Simader,*Weak solutions of the Dirichlet problem for strongly nonlinear elliptic differential equations*, Math. Z. 150 (1) (1976) pp. 1-26. MR**54:8018****11.**J.R.L. Webb,*On the Dirichlet problem for strongly nonlinear elliptic operators in unbounded domains*, J. Lond. Math. Soc. 10 (1975) pp. 163-170. MR**52:14644**

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Additional Information

**J. Berkovits**

Affiliation:
Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014 Oulu, Finland

Email:
juha.berkovits@oulu.fi

DOI:
https://doi.org/10.1090/S0002-9939-03-07094-1

Keywords:
Compact imbedding

Received by editor(s):
May 30, 2002

Published electronically:
April 9, 2003

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2003
American Mathematical Society