منابع مشابه
Strictly Semi-transitive Operator Algebras
An algebra A of operators on a Banach space X is called strictly semitransitive if for all non-zero x, y ∈ X there exists an operator A ∈ A such that Ax = y or Ay = x. We show that if A is norm-closed and strictly semi-transitive, then every A-invariant linear subspace is norm-closed. Moreover, LatA is totally and well ordered by reverse inclusion. If X is complex and A is transitive and strict...
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Partial orders and the clones of functions preserving them have been thoroughly studied in recent years. The topic of this papers is strict orders which are irreflexive, asymmetric and transitive subrelations of partial orders. We call an algebra A = (A,Ω) strictly order primal if for some strict order (A,<) the term functions are precisely the functions which preserve this strict order. Our ap...
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The genesis of this paper is the construction of a new operator that, when combined with a theorem of Herrero, settles a question of Herrero. Herrero proved that a strictly cyclic operator on an infinite dimensional Hilbert space is never triangular. He later asks whether the adjoint of a strictly cyclic operator is necessarily triangular. We settle the question by constructing an operator T fo...
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An example is given of a unilateral weighted shift on complex Hubert space which is strictly cyclic but not strongly strictly cyclic. Similar examples of weighted shifts on the sequence spaces lp, for 1 < p < oo, are indicated.
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Notice that the left-hand side of the third equation is the sum of the left-hand sides of the first two. As a result, no solution to the system exists unless a + b = c. But if a + b = c, then any solution of the first two equations is also a solution of the third; and in any linear system involving more unknowns than equations, solutions, when they exist, are never unique. In the present case, ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1991
ISSN: 0002-9947
DOI: 10.2307/2001659