Strongly nonnorming subspaces and prequojections

Moscatelli, V. B.

doi:10.4064/sm-95-3-249-254

Cited by 13 publications

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“…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]. All of these papers employ the same method, which consists in the construction of the dual of a prequojection, rather than the prequojection itself, which is often difficult to describe (see the survey paper [29] for further information).…”

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

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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.

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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

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“…Recall that a Fréchet space X is called a quojection if, for every continuous seminorm p on X , the space X/Kerp is Banach when endowed with the quotient topology. It is easily seen that X is a quojection if it is isomorphic to the projective limit of a sequence of Banach spaces with respect to surjective mappings [7].…”

Section: Preliminariesmentioning

confidence: 99%

Fréchet-Hilbert spaces and the property SCBS

2018

Turk J Math

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In this note, we obtain that all separable Fréchet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioglu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Fréchet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Fréchet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Fréchet-Hilbert space still takes place up to a complemented Hilbert subspace. Moreover, the strong dual of a real Fréchet-Hilbert space has the SCBS property.

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“…Theorem 3 gives tSe negative answer to ihe following question posed in Remark 5 of [7, p. In [8] when proving Theorern 4 in tSe particular case E = (co) 1V V.B. Moscatelli proved ihe following resulí:…”

Section: Arad (P'fi(f'f)) Ja Isomorpitic Lo Jnd»g(n)mentioning

confidence: 99%

“…D. Vogt [141shows the relevance of quojections arad prequojections in conraection with the sp]itting of exact sequences of Fréchet spaces. Ira the present paper we coratinne investigatioras of [8], ¡7] of the structure of strorag dnals of prequojectioras with continuous norma. In addition we introduce a class of prequojectioras which we cal!…”

Section: And E Dubirasky ¡2] Ira Their Study Of Fréchet Spaces With mentioning

confidence: 99%

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On prequojections and their duals

Ostrovskii¹

1998

Rev. Mat. Complut.

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Tbe paper is devoted to the class of Fréchet spaces which are called prequojections. This class appeared in a natural way in tSe structure theory of Fréchet spaces. TSe structure of prequojections was studied by G. Metafune and V.B. Moscatelli, who also gaye a survey of tSe subject. Answering a qu~tion of these authors we show tbat their result on duals of prequojections cannot be generahized from the separable case to the case of spaces of arbitrary cardinality. Wc also introduce a special class of prequojections, we calI them canonical, and show that in tSe main result of G. Metafune and V.B. Moscatelli on tSe existence of a prequojection with a given dual we may require this prequojection to be a canonical one.The main purpose of tuis paper is to iravestigate a class of Fréchet spaces which are called prequojections. This class appeared naturally iii tSe development of the structure theory of Fréchet spaces.Let us recail sorne definitions. A Fréchet space F is called a quojection if there exists a sequerace {P»J~of Banach spaces aud a sequence of linear continuous surjective mappings 1?,, P».~~14, (n E IV) such that F is isomorphic to the projective limit projn (Fn,1?»). According to [6]

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Strongly nonnorming subspaces and prequojections

Cited by 13 publications

References 0 publications

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

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

Fréchet-Hilbert spaces and the property SCBS

On prequojections and their duals

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