On Banach spaces of strongly convergent trigonometric series

On Banach spaces of absolutely and strongly convergent Fourier series

“…Statements (i) through (iii) are contained in Theorem 1, Lemma 1 and Remark 1 in [10]. Statements (iv) and (v) follow from Theorems 2 and 3 in [10].…”

“…Here C~ denotes the Ces~ro method of order 1. In the following theorem we collect some of the properties of these classes established in [6] and [10]. From Theorem 4 in [7] it follows that ~r properly.…”

“…These concepts have already been applied to trigonometric and Fourier series in [5] through [10]. These concepts have already been applied to trigonometric and Fourier series in [5] through [10].…”

“…Although the essential properties of the classes 5 a~ are established by Theorem B and other results proved in [6] and [10], it is natural, in view of (i), (iii) and (iv) of Theorem B, to investigate other norms expressed in terms of the coefficients and the q/-norm.…”

Strong Boundedness and Strong Convergence in Sequence Spaces

“…• An FK-space E has the property of strong convergence if and only if E = t vo • E. The concept of strong convergence [/] was investigated both in summability theory [8], [1], [9], [10] and Fourier analysis [13], [14], [15], [16], [17]. This generated new classes of interesting sequence spaces and spaces of Fourier series.…”