Study On The K-theory Of Operator Algebra On G-M Type Space

Master thesis " Study on the K-group of operator algebra on G-M type spaces " is the organic combinative result of the study on the theory of Banach space and the operator theory of functional analysis.There are four chapters in the paper. Chapter 1 mainly introduces some basic results about the paper, including some conceptions and notations needed in the following chapters. In chapter 2,we discuss the K-group of Wiener algebra W and show that K₀(W) = Z and K₁(W) = Z. Chapter 3 and chapter 4 is the main works of this paper, we mainly study the K-group of operator algebra on the rth shift spaces.In chapter 3,we compute the K-group of operator algebra on the 1th shift space X_GM2:K₀(B(X_GM2)) = Z,K₁(B(X_GM2)) = {0}.In chapter 4, we compute the K-group of operator algebra B(X_S^r)on the rth(r ≥ 2) shift space X_S^r: K₀(B(X_S^r)) = Z (?) Z_r, K₁(B(X_S^r)) = {0}.