The space B(pi) and its dual

• Main Authors: Po-chin Yang, 楊柏青
• Other Authors: Mark C. Ho
• Format: Others
• Language: en_US
• Online Access: http://ndltd.ncl.edu.tw/handle/96728357063112424613

碩士 === 國立中山大學 === 應用數學系研究所 === 92 === The space B(pi), defined by s.n. function (Phi)(pi)(x_{1},...), were discussed in details in [8], and it is shown that B(pi) is the dual space of B(Pi)^0, which is the closure of the polynomials in B(Pi), the space of analytic function defined by the s.n. function (Phi)(Pi)(x_{1},...), provided that {pi_{n}} satisfies some regularity condition. In this article, we will show that in fact we have the relation (B(Pi)^0)^* approx B(pi), B(pi)^* approx B(Pi). This is an interesting analogy to the classical duality between the operator ideal (S(Pi))^(0), S(pi) and S(Pi), or, the s.n. ideal defined by (Phi)(Pi) and (Phi)(pi).