Bessaga's conjecture in unstable Köthe spaces and products

Zefer Nurlu; Jasser Sarsour

Displaying similar documents to “Bessaga's conjecture in unstable Köthe spaces and products”

Characterization of subspaces and quotients of nuclear $L_{f} (α, \infty)$ -spaces

Heikki Apiola (1983)

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Basic sequences in (s)

Ed Dubinsky (1977)

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Basic sequences in stable infinite type power series spaces

M. Alpseymen (1981)

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Some remarks on Dragilev's theorem

C. Bessaga (1968)

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Quotient spaces of (s) with basis

Ed Dubinsky, William Robinson (1978)

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Grothendieck-Lidskiĭ theorem for subspaces of quotients of $L_{p}$ -spaces

Oleg Reinov, Qaisar Latif (2014)

Banach Center Publications

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Generalizing A. Grothendieck’s (1955) and V. B. Lidskiĭ’s (1959) trace formulas, we have shown in a recent paper that for p ∈ [1,∞] and s ∈ (0,1] with 1/s = 1 + |1/2-1/p| and for every s-nuclear operator T in every subspace of any $L_{p} (ν)$ -space the trace of T is well defined and equals the sum of all eigenvalues of T. Now, we obtain the analogous results for subspaces of quotients (equivalently: for quotients of subspaces) of $L_{p}$ -spaces.

Unsolved Problems

N. Aronszajn, L. Gross, S. Kwapień, N. Nielsen, A. Pełczyński, A. Pietsch, L. Schwartz, P. Saphar, S. Chevet, R. Dudley, D. Garling, N. Kalton, B. Mitjagin, S. Rolewicz, E. Schock, J. Daleckiĭ, J. Dobrakov, B. Gelbaum, G. Henkin, L. Nachbin, N. Peck, L. Waelbroeck, P. Porcelli, M. Rao, M. Zerner, V. Zakharjuta (1970)

Studia Mathematica

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1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483

Superspaces of (s) with basis

Lasse Holmström (1983)

Studia Mathematica

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Tameness in Fréchet spaces of analytic functions

Aydın Aytuna (2016)

Studia Mathematica

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A Fréchet space with a sequence ${| | \cdot | |}_{k}_{k = 1}^{\infty}$ of generating seminorms is called tame if there exists an increasing function σ: ℕ → ℕ such that for every continuous linear operator T from into itself, there exist N₀ and C > 0 such that ${| | T (x) | | ₙ \leq C | | x | |}_{σ (n)}$ ∀x ∈ , n ≥ N₀. This property does not depend upon the choice of the fundamental system of seminorms for and is a property of the Fréchet space . In this paper we investigate tameness in the Fréchet spaces (M) of analytic functions on Stein manifolds M equipped...

Every nuclear Fréchet space with a regular basis has the quasi-equivalence property

Lawrence Crone, William Robinson (1975)

Studia Mathematica

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Topological classification of strong duals to nuclear (LF)-spaces

Taras Banakh (2000)

Studia Mathematica

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We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: $ℝ^{ω}$ , $ℝ^{\infty}$ , $Q \times ℝ^{\infty}$ , $ℝ^{ω} \times ℝ^{\infty}$ , or ${(ℝ^{\infty})}^{ω}$ , where $ℝ^{\infty} = l i m ℝ^{n}$ and $Q = {[- 1, 1]}^{ω}$ . In particular, the Schwartz space D’ of distributions is homeomorphic to ${(ℝ^{\infty})}^{ω}$ . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to $ℝ^{\infty}$ or to $Q \times ℝ^{\infty}$ . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic...

A new definition of nuclear systems with applications to bases in nuclear spaces

Ed Dubinsky (1972)

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The tensor algebra of power series spaces

Dietmar Vogt (2009)

Studia Mathematica

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The linear isomorphism type of the tensor algebra T(E) of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always s, the situation for finite type power series spaces is more complicated. The linear isomorphism T(s) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra $s_{•}$ . This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet...