For a scalar sequence (theta(n))(n is an element of N), let C be the matrix defined by c(n)(k) = theta(n-k+1) if n >= k, c(n)(k) = 0 if n < k. The map between Kothe spaces lambda(A) and lambda(B) is called a Cauchy Product map if it is determined by the triangular matrix C. In this note we introduced some necessary and sufficient conditions for a Cauchy Product map on a nuclear Kothe space lambda(A) to nuclear G(1) - space lambda(B) to be linear and continuous. Its transpose is also considered.


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...
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.
A remark on a paper of P. B. Djakov and M. S. Ramanujan
Uyanik, Elif; Yurdakul, Murat Hayrettin (2019-01-01)
Let l be a Banach sequence space with a monotone norm in which the canonical system (e(n)) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-Kothe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Kothe matrices when every continuous linear operator between l-Kothe spaces is bounded. As an application, we observe that the existence of an unbounded operator between l-Kothe ...
Conformal vector fields with respect to the Sasaki metric tensor field
Şimşir, Fatma Muazzez; Tezer, Cem; Department of Mathematics (2005)
On the tangent bundle of a Riemannian manifold the most natural choice of metric tensor field is the Sasaki metric. This immediately brings up the question of infinitesimal symmetries associated with the inherent geometry of the tangent bundle arising from the Sasaki metric. The elucidation of the form and the classification of the Killing vector fields have already been effected by the Japanese school of Riemannian geometry in the sixties. In this thesis we shall take up the conformal vector fields of the ...
A note on the Gauss maps of Cayley-free embeddings into spin(7)-manifolds
Ünal, İbrahim (Elsevier BV, 2018-12-01)
We show that a closed, orientable 4-manifold M admits a Cayley-free embedding into flat Spin(7)-manifold R-8 if and only if both the Euler characteristic chi(M) and the signature tau(M) of M vanish.
Citation Formats
E. Uyanik and M. H. Yurdakul, “A NOTE ON TRIANGULAR OPERATORS ON SMOOTH SEQUENCE SPACES,” OPERATORS AND MATRICES, pp. 343–347, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30105.