Sequence Spaces and Summability Factors.
Some analogues of Knopp's core theorem.
Spectral decompositions, ergodic averages, and the Hilbert transform
Let U be a trigonometrically well-bounded operator on a Banach space , and denote by the sequence of (C,2) weighted discrete ergodic averages of U, that is, . We show that this sequence of weighted ergodic averages converges in the strong operator topology to an idempotent operator whose range is x ∈ : Ux = x, and whose null space is the closure of (I - U). This result expands the scope of the traditional Ergodic Theorem, and thereby serves as a link between Banach space spectral theory and...
Statistically strongly regular matrices and some core theorems.
Strongly Almost Convergent Sequences
Strongly almost convergent sequences.
Strongly summable sequences defined over real -normed spaces.
Sublinear functionals and KnoppJs core theorem.
Summable families in nuclear groups
Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.
Summable subsequences in convergence groups
Sur La Perfection Des Procédés Continus Permanents
Sur la perfection des procédés continus permanents.