Weakly unconditionally Cauchy series and Fibonacci sequence spaces

Weakly unconditionally Cauchy series and Fibonacci sequence spaces

We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in [Formula: se...

Characterizations of Series in Banach Spaces

In this paper we prove several new characterizations of weakly unconditionally Cauchy series in Banach spaces and in the dual space of a normed space. For a given series ζ, we consider the spaces S(ζ), Sw(ζ) and S0(ζ) of bounded sequences of real numbers (ai)i such that the series P i aixi is convergent, weakly convergent or ∗-weakly convergent, respectively. By means of these spaces we charact...

A Class of Convergent Series with Golden Ratio Based on Fibonacci Sequence

In this article, a class of convergent series based on Fibonacci sequence is introduced for which there is a golden ratio (i.e. $frac{1+sqrt 5}{2}),$ with respect to convergence analysis. A class of sequences are at first built using two consecutive numbers of Fibonacci sequence and, therefore,  new sequences have been used in order  to introduce a  new class of series. All properties of the se...

Compact operators on some Fibonacci difference sequence spaces

*Correspondence: [email protected] 1Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Abstract In this paper, we characterize the matrix classes ( 1, p(F)) (1≤ p <∞), where p(F) is some Fibonacci di...

ε-weakly Chebyshev subspaces and quotient spaces