No abstract

No abstract

Abstract. In this paper, the random bounded operators from a Banach space X into a Banach space Y and the problem of extending random operators are investigated. It is shown that unlike the deterministic bounded operators, the random version of the principle of uniform boundedness and the Banach-Steinhaus theorem do not hold for random bounded operators. In addition, a random operator can be extended to apply to all random inputs if and only if it is bounded. As a consequence, we conclude that the Ito stochastic integral cannot be extended in a natural fashion to all random functions with square-integrable sample paths.

To cite this article: Dang hung Thang (1995) The adjoint and the composition of random operators on a hilbert space, Stochastics and Stochastic Reports, 54:1-2, 53-73To link to this article: http://dx.In thic papcr. the adjoin: and the conlposition of random operators arc: defined in a natural fashion. . T uillrbc v:... uCrr;,tit&.:ic 2 ....-. :. operators, the adjoint and !he romposition nccd not exist in general. Various .;i?nJitie~r -.n.s!!ring rheir existence as well as many examples are provided KEY WORDS: Random operators, the random adjoint opeiziiirr. ihi composition of ranJom operators, ( A . r)-applicable random variables, (9,,)-predictable sequences.

No abstract

No abstract

No abstract

No abstract