Operator-valued multiplier theorems characterizing Hilbert spaces
نویسندگان
چکیده
منابع مشابه
Operator-valued bases on Hilbert spaces
In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...
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let $x,y$ be normed spaces with $l(x,y)$ the space of continuous linear operators from $x$ into $y$. if ${t_{j}}$ is a sequence in $l(x,y)$, the (bounded) multiplier space for the series $sum t_{j}$ is defined to be [ m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}% t_{j}x_{j}text{ }converges} ] and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...
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in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also de ne the concepts of bessel, hilbert ov-basis and obt...
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Let X,Y be locally convex spaces and L(X,Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series P Tk in L(X,Y ). First, if λ is a scalar sequence space, we say that the series P Tk is λ multiplier convergent for a locally convex topology τ on L(X,Y ) if the series P tkTk is τ convergent for every t = {tk} ∈ λ. We establish...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2004
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700013550