Continuous Operators on Paranormed Spaces and Matrix Transformations of Strong Cesaro Summable Sequences

Authors : E BULUT

Pages : 0-0

Doi:10.1501/Commua1_0000000279

View : 11 | Download : 8

Publication Date : 1978-01-01

Article Type : Research Paper

Abstract :is paper, the concept of a paranormed fi.-space is definede where ? X> 1 is aninteger, and two Banach-Steinhaus type theorems are proved for the sequences of continuous linear ûınctionals on such space. For example, the necessary and sufficient conditions are given for a sequence insert ignore into journalissuearticles values(A n insert ignore into journalissuearticles values(x );); of continuous linear functionals to be in the space of generalized entire sequences, for each x belonging to a paranormed fi-speace. These results are then used to characterize the matrix transformations between the strong Cesaro summble sequence space w insert ignore into journalissuearticles values(p); and the space of generalized entire sequences.
Keywords : Operators, Paranormed, Spaces