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Sequence Spaces with Oscillating Properties

✍ Scribed by Johann Boos; Daniel J. Fleming; Toivo Leiger

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
222 KB
Volume
200
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this note we consider various types of oscillating properties for a sequence space E being motivated by an oscillating property introduced by Snyder and by recent papers dealing with theorems of Mazur᎐Orlicz type and gliding hump properties. Our main tools, two summability theorems, allow us to identify two such oscillating properties for a sequence space E one of which provides a sufficient condition for E ; F to imply E ; W while the other affords a sufficient F condition for E ; F to imply E ; S . Here F is any L -space, a class of spaces F which includes the class of separable FK-spaces, S denotes the elements of F F having sectional convergence, and W denotes the elements of F having weak F sectional convergence. This, in turn, is applied to yield improvements on some other theorems of Mazur᎐Orlicz type and to obtain a general consistency theorem. Furthermore, combining the above observations with the work of Bennett and Kalton we obtain the first oscillating property on a sequence space E as a

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