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 t.....

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