Frechet-Hilbert spaces and the property SCBS

In this note, we obtain that all separable Frechet-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 Frechet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Frechet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Frechet-Hilbert space still takes place up to a complemented Hilbert subspace. Moreover, the strong dual of a real Frechet-Hilbert space has the SCBS property.


Factorization of unbounded operators on Kothe spaces
Terzioglou, T; Yurdakul, Murat Hayrettin; Zuhariuta, V (2004-01-01)
The main result is that the existence of an unbounded continuous linear operator T between Kothe spaces lambda(A) and lambda(C) which factors through a third Kothe space A(B) causes the existence of an unbounded continuous quasidiagonal operator from lambda(A) into lambda(C) factoring through lambda(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (lambda(A), lambda(B)) ...
BASKAL, S; ERIS, A; SATIR, A (1994-12-19)
The symmetries and associated conservation laws of the SO(2,1) invariant non-linear sigma model equations in 1+1 dimensions are investigated. An infinite family of generalized local symmetries is presented and the uniqueness of these solutions is discussed.
Some finite-dimensional backward shift-invariant subspaces in the ball and a related factorization problem
Alpay, D; Kaptanoglu, HT (2000-12-15)
Beurling's theorem characterizes subspaces of the Hardy space invariant under the forward-shift operator in terms of inner functions. In this Note we consider the case where the ball replaces the open unit desk and the reproducing kernel Hilbert space with reproducing kernel 1/(1-Sigma (N)(1) a(j)w(j)*) replaces the Hardy space. We give explicit formulas which generalize Blaschke products in the case of spaces of finite codimension. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier...
Bounded operators and complemented subspaces of Cartesian products
DJAKOV, PLAMEN; TERZİOĞLU, AHMET TOSUN; Yurdakul, Murat Hayrettin; Zahariuta, V. (2011-02-01)
We study the structure of complemented subspaces in Cartesian products X x Y of Kothe spaces X and Y under the assumption that every linear continuous operator from X to Y is bounded. In particular, it is proved that each non-Montel complemented subspace with absolute basis E subset of X x Y is isomorphic to a space of the form E(1) x E(2), where E(1) is a complemented subspace of X and E(2) is a complemented subspace of Y. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Equivariant cross sections of complex Stiefel manifolds
Onder, T (Elsevier BV, 2001-01-16)
Let G be a finite group and let M be a unitary representation space of G. A solution to the existence problem of G-equivariant cross sections of the complex Stiefel manifold W-k(M) of unitary k-frames over the unit sphere S(M) is given under mild restrictions on G and on fixed point sets. In the case G is an even ordered group, some sufficient conditions for the existence of G-equivariant real frame fields on spheres with complementary G-equivariant complex structures are also obtained, improving earlier re...
Citation Formats
E. Uyanik and M. H. Yurdakul, “Frechet-Hilbert spaces and the property SCBS,” TURKISH JOURNAL OF MATHEMATICS, pp. 1294–1297, 2018, Accessed: 00, 2020. [Online]. Available: