ACCRETIVE OPERATORS AND BANACH ALAOGLU THEOREM IN LINEAR 2-NORMED SPACES

Authors

  • P. K. Harikrishnan Manipal Institute of Technology.
  • Bernardo De La Fuerza Universidad de Almería.
  • K. T. Ravindran Payyanur College.

DOI:

https://doi.org/10.4067/S0716-09172011000300004

Keywords:

Linear 2, Normed spaces, Sequentially closed, Accretive operators, Weak compact, Homeomorphism, Banach Alaoglu theorem.

Abstract

In this paper we introduce the concept of accretive operator in linear 2-normed spaces, focusing on the relationships and the various aspects of accretive, m-accretive and maximal accretive operators. We prove the analogous of Banach-Alaoglu theorem in linear 2- normed spaces, obtaining an equivalent definition for accretive operators in linear 2-normed spaces.

References

[1] Berbarian, Lectures in Operator theory, Springer, 1973.

[2] Fatemeh Lael and Kourosh Nourouzi, Compact Operators Defined on 2-Normed and 2-Probabilistic Normed Spaces, Hindawi Publishing Corporation,Mathematical Problems in Engineering, Volume 2009 (2009), Article ID 950234, 17 pages.

[3] Raymond W. Freese,Yeol Je Cho, Geometry of linear 2-normed spaces, Nova Science publishers, Inc, Newyork, (2001).

[4] Shih a“ sen Chang, Yeol Je Cho, Shin Min Kang, Nonlinear operator theory in Probabilistic Metric spaces, Nova Science publishers, Inc, Newyork, (2001).

[5] S. Gahler, Siegfried 2-metrische Raume und ihre topologische struktur, Math. Natchr. 26(1963),115-148.

[6] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, Vol. 19, No. 4, (1967).

Published

2011-12-10

How to Cite

[1]
P. K. Harikrishnan, B. De La Fuerza, and K. T. Ravindran, “ACCRETIVE OPERATORS AND BANACH ALAOGLU THEOREM IN LINEAR 2-NORMED SPACES”, Proyecciones (Antofagasta, On line), vol. 30, no. 3, pp. 319-327, Dec. 2011.

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