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Additional resources for Integral Equations and Operator Theory - Volume 67
Example text
6, Theorem 6]). Recently, Argyros and Haydon constructed a real HI space X with the property that every operator on X takes the form λI + K, where K is compact [1]. 2. Given these facts, the next questions seem natural to us. 2. Is it possible to find an operator of the form I + T , where T is strictly singular or even compact, such that AI+T is non-empty and nondense? In particular, can such an operator exist on Argyros–Haydon space? 2 have negative solutions then this would suggest to us that some kind of unconditional structure is necessary in order to construct such operators.
Result and Proof The main result in this paper reads as follows. 1. Let L be a subspace lattice on a Banach space X and suppose that ∨{F : F ∈ J (L)} = X or ∧{F− : F ∈ J (L)} = (0). Let δ : AlgL → B(X) be a Jordan derivation. Then δ is a derivation. To prove the theorem, we need some lemmas. 2. Let x⊗f be in AlgL and suppose that f (x) = 1. Then δ(x ⊗ f ) ker(f ) ⊆ Fx. Proof. Indeed, from δ(x ⊗ f ) = δ((x ⊗ f )2 ) = (x ⊗ f )δ(x ⊗ f ) + δ(x ⊗ f )(x ⊗ f ), we easily see that δ(x ⊗ f ) ker(f ) ⊆ Fx.
Orbits, weak orbits and local capacity of operators. Integral Equ. Oper. : Orbits of operators. , Le´ on-Saavedra, F. ) Advanced Courses of Mathematical Analysis I, pp. 53–79. : Orbits of linear operators tending to infinity. Rocky Mountain J. Math. : The geometry of an orbit. : On orbits of elements. Studia Math. : On Banach spaces with unconditional bases. Israel J. Math. cz Richard J. ie Received: May 31, 2009. Revised: January 12, 2010. Integr. Equ. Oper. 1007/s00020-010-1767-x Published online April 13, 2010 c Birkh¨ auser / Springer Basel AG 2010 Integral Equations and Operator Theory Existence Results for Fractional Order Semilinear Integro-Differential Evolution Equations with Infinite Delay Yong Ren, Yan Qin and R.
Integral Equations and Operator Theory - Volume 67 by C. Tretter (Chief Editor)
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