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| Abstract : Universiti Pendidikan Sultan Idris |
| Let a pair , X be functional calculus, where is a homomorphism from the space of the
measurable functions on , into the space of all linear bounded operators LB X , X on a
reflexive Banach space X . We define a norm of functional calculus by , , ,supL X Xf ff 1
, the convergence of the sequence of functional calculi is a
convergence relative to this norm. We study the correspondence between sequences of spectral
decompositions, well-bounded operators n A defined on the reflexive Banach space X , and
their correspondence with the theory of functional calculus for such operators. In this article,
we establish that if a sequence of the projection-valued measures , nE I strongly
converges to E , I then the sequence n of the functional calculi converges to
the functional calculus . Results of the article can be employed in the modern extensions of
the quantum theory and theory of quantum information.
Keywords: functional calculus, projection-valued measure, projection operator, measurable
calculus |
| References |
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