Fa-summability and Fa-core

This thesis has three chapters. In the first chapter some preliminary definitions, concepts and theorems are given which will be useful in the next chapters. In the first part of the second chapter which is the first original part of thesis, in the special case of A, the relations between the spaces c, Va and the space (Fa) introduced by Lorentz are given. Further, the infinite matrix transforming the spaces m, c, F and Va into the space (Fa) are characterized. In the second part, F^-core of a bounded number sequence is defined and the relations between the concepts F^-core and well-known Knoop (K), Banach (B), cr-cove are investigated. In the first part of the final chapter, necessary and sufficient conditions for a matrix B to yield FA-cove(Bx) Ç K-cove(x), FA-cove(Bx) Ç B-core(x) and Fa- cove(Bx) C er-core(a;) for all x 6 m are determined. In the second part, necessary and sufficient conditions are determined in order to K-cove(Ax) Ç K-core(Rx), FA-core(Bx) Ç K-cove(Rx), FA-cove(Bx) Ç B-cove(Rx) and FA-core(5a;) Ç a- coxe(Rx) for all x £ m, where R is the matrix of the particular summability method Riesz. IV V -