Matrix summability and uniform convergence of series

Aizpuru, A.; García-Pacheco, Francisco Javier; Pérez-Eslava, C.

doi:10.1090/s0002-9939-07-08882-x

Cited by 7 publications

(8 citation statements)

References 13 publications

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“…The reader may immediately realize that The previous theorem is still valid if we change almost convergence for weak almost convergence. Also, the previous theorem generalizes Theorem 3.2.2 and some other results in [7,8,11,25] for sequences in X (c 0 ) by means of (weak) almost convergence summability methods.…”

Section: Multiplier Spaces Of Almost Summing Sequencessupporting

confidence: 68%

“…Theorem 3.2.2 (Swartz, 1983; [66]) If X is a Banach space and (x n ) n∈N is a sequence in X(ℓ ∞ ) such that lim n→∞ ∞ i=1 a i x n i exists in X for each (a i ) i∈N ∈ ℓ ∞ , then there exists x 0 ∈ X(ℓ ∞ ) such that lim n→∞ x n − x 0 m = 0 in X(ℓ ∞ ). Extensions of the previous theorem have been obtained in [7,8,11] for wuC series.…”

Section: The Spaces X (S) and X W (S)mentioning

confidence: 79%

See 1 more Smart Citation

Vector-Valued Banach Limits and Vector-Valued Almost Convergence

Garcia-Pacheco,

Perez-Fernandez

2018

Preprint

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This book was intended to be Rafael Armario's Ph.D. thesis dissertation for obtaining his doctoral degree in Pure Mathematics at the University of Cádiz (Spain, EU). Unfortunately he passed away on January 28 th , 2013, right after he started writing this manuscript. His two Ph.D. advisors at the time of his death (the authors of this book) decided then to finish his work in book format and this is how this manuscript was given birth. Rafael Armario's lifeRafael Armario, better known as "Rafa" by his friends, was a joyful and warm person, a beloved son and friend, a very hard-working graduate student, an excellent highschool teacher, and an extremely brilliant mathematician. Childhood and early lifeRafa was born and raised in Cadiz, the oldest European city, within a humble middleclass family. He quickly developed a strong interest in the Cadiz culture and folklore, in particular, in the worldwide famous Cadiz carnival. Other local feasts such as the El Puerto fair also grew on him in a very profound way. University of Cadiz undergraduate periodRafa decided to register as a math major in the university of Cadiz after graduating from his neighborhood high school. He met a lot of friends there among students and i ii PREFACE professors, including the one who left the strongest imprint on him, Prof. Antonio Aizpuru, who eventually became his Ph.D. advisor. He also met a bunch of friends a buddies like Fernandito, Mari, Sole, Marina, Marimar, el Gafas, etc. Rafael Armario's workDuring his working period as a top-level mathematician, Rafa accomplished many objectives and obtained many different results. Indeed, all the theorems, definitions, examples, etc., which are anonymous in this book (including those of the framework) are due to his joint work with Prof. Aizpuru and the authors of this manuscript. University of Cadiz graduate periodRafa's graduate period was undoubtedly conditioned by the death of his Ph.D. advisor at the time, Prof. Antonio Aizpuru, who passed away in March 2008 after Rafa and him published their first paper (see [5]), which was also co-authored by his Ph.D. co-advisor at the time, Prof. Francisco Javier Pérez-Fernández.In September 2010, Prof. García-Pacheco, better known as Paquito, was hired at the level of Assistant Professor by the Mathematics Department of the University of Cadiz after spending nine semesters (three American academic years) at Kent State University (Ohio, USA) and ten semesters at Texas A&M University (Texas, USA). One of the first assignments of Prof. García-Pacheco was to co-advice Rafael Armario together with Prof. Pérez-Fernández, continuing this way the work once started by Prof. Antonio Aizpuru. The fruit of this co-advising was the co-authorship of the papers [3, 4,12,13,40]. The present book consists of those papers.Many anecdotes occurred during his graduate school period. For instance, in one occasion, Rafa and Paquito shared a hotel room, due to a lack of research funding, while attending a conference held in the university of Almeria (Spain, EU). The hotel wor...

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Section: Multiplier Spaces Of Almost Summing Sequencessupporting

confidence: 68%

Section: The Spaces X (S) and X W (S)mentioning

confidence: 79%

Vector-Valued Banach Limits and Vector-Valued Almost Convergence

Garcia-Pacheco,

Perez-Fernandez

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…Next, we will prove the main result that, in a way, mimics some ideas that appear in [5,15]. It is surprising how this result unifies all known results and it applies to most summability methods.…”

Section: Schur Lemma Through Summability Methodssupporting

confidence: 61%

“…In Section 4, we will obtain a general Schur-type lemma for general summability methods; thus, we unify results appeared in [5,15], and finally we close the paper with a brief section with concluding remarks and open questions.…”

Section: Introductionmentioning

confidence: 92%