Some new results on commutative Algebra Dr. Singh Abhik* Department of Mathematics, Patna University, Patna, Bihar- 800005, India *Corresponding Author: Dr. Abhik Singh, Department of Mathematics, Patna University, Patna, Bihar-800005, India E-mail: abhik51@gmail.com
Online published on 6 July, 2022. Abstract In this paper, we shall discuss and give applications of a polarization formula, which yields estimates of xx… … … … …xn when estimates of xn are given, and estimates of the polarized forms of the terms of the Taylor expansion of a bounded holomorphic function over a bell in Banach space. The polarization formula can be used to obtain new properties of commutative algebras, with a convex topology or a convex bounded structure. The polarization formula will be proved in the first section, a few application will be given in section 2,3,4 in which we obtain estimates of x1… … … … …xn from estimates of xn. We shall also define the infinite dimensional holomorphic functional calculus. Top Keywords Polarization, Convex Algebra, Equiregular. Top |