Unbounded linear operators and nuclear Köthe quotients

Önal, Süleyman; Terzioğlu, Tosun

doi:10.1007/bf01188687

Cited by 14 publications

(9 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall that a Fréchet space is not a prequojection if and only if it admits a separated quotient isomorphic to an infinite dimensional nuclear Köthe echelon space, see [5,14,33,37]. This fact, together with Propositions 3.2 and 3.4, suggest the following Question 1.…”

Section: Proposition 34 Let X Be a Prequojection Fréchet Space Thementioning

confidence: 90%

“…It is known that X is a prequojection if and only if X β is a strict (LB)-space. An alternative characterization is that X is a prequojection if and only if X has no nuclear quotient which admits a continuous norm, see [5,14,33,37]. The problem of the existence of non-trivial prequojections arose in a natural way in [5]; it has been solved, in the positive sense, in various papers, [6,14,32].…”

Section: Proposition 32mentioning

confidence: 98%

See 1 more Smart Citation

C0-semigroups and mean ergodic operators in a class of Fréchet spaces

Albanese

Bonet

Ricker

2010

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

It is shown that the generator of every exponentially equicontinuous, uniformly continuous C 0 -semigroup of operators in the class of quojection Fréchet spaces X (which includes properly all countable products of Banach spaces) is necessarily everywhere defined and continuous. If, in addition, X is a Grothendieck space with the Dunford-Pettis property, then uniform continuity can be relaxed to strong continuity. Two results, one of M. Lin and one of H.P. Lotz, both concerned with uniformly mean ergodic operators in Banach spaces, are also extended to the class of Fréchet spaces mentioned above. They fail to hold for arbitrary Fréchet spaces.

show abstract

Section: Proposition 34 Let X Be a Prequojection Fréchet Space Thementioning

confidence: 90%

Section: Proposition 32mentioning

confidence: 98%

C0-semigroups and mean ergodic operators in a class of Fréchet spaces

Albanese

Bonet

Ricker

2010

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…The following two notions, introduced in [22,23,30], are defined here in a slightly different equivalent form.…”

Section: (P)mentioning

confidence: 99%

On some normability conditions

Terzioğlu

Yurdakul

Zahariuta

2005

Mathematische Nachrichten

View full text Add to dashboard Cite

Various normability conditions of locally convex spaces (including Vogt interpolation classes DNϕ and Ωϕ as well as quasi-and asymptotic normability) are investigated. In particular, it is shown that on the class of Schwartz spaces the property of asymptotic normability coincides with the property GS, which is a natural generalization of Gelfand-Shilov countable normability (cf. [9,25], where the metrizable case was treated). It is observed also that there are certain natural duality relationships among some of normability conditions.

show abstract

“…Quojections are important tools in Fréchet spaces theory. Recall that, by the results of S. F. Bellenot and E. Dubinsky [1], D. Vogt [24], and S.Önal and T. Terzioǧlu [10], a Fréchet space E has a nuclear Köthe quotient if and only if the strong bidual of E is not quojection (compare with Theorem 3.4).…”

Section: Introductionmentioning

confidence: 98%