Some new Cesàro sequence spaces of order α

UDC 517.98 We introduce the spaces ℓ ∞ ( C α ) , f ( C α ) , and f 0 ( C α ) of Ces\`{a}ro bounded, Ces\`{a}ro almost convergent, and Ces\`{a}ro almost null sequences of order α , respectively. Moreover, we establish some inclusion relations for these spaces and determine the α -, β - and γ -duals of the spaces ℓ ∞ ( C α ) and f ( C α ) . Finally, we characterize the classes of matrix transformations from the space f ( C α ) to any sequence space Y and from any sequence space Y to the space f ( C α ) .