STABILITY THEOREMS OF THE OPERATOR-VALUED FUNCTION SPACE INTEGRAL ON $C_0(B)$

Abstract

In 1968, Cameron and Storvick introduce the definition and the theories of the operator-valued function space integral. Since then, the stability theorems of the integral was developed by Johnson, Skoug, Chang etc [1, 2, 4, 5]. Recently, the authors establish the existence theorem of the operator-valued function space [8]. In this paper, we will prove the stability theorems of the operator-valued function space integral over paths in abstract Wiener space $C_0(B)$.

Keywords

• abstract Wiener space;
• scale-invariant measurable subset;
• (s-w)-integral

File

Download PDF

References

1. Gaussian Random Field Stability theorems for the operator-valued function space integral K. S. Chang;K. S. Ryu
2. Supplemento ai Rendiconti del Circolo Mathematico di Palermo. Serie Ⅱ v.17 Stability theorems for the Feynman integral ; The L(L₁(R), Co(R)) theory J. S. Chang
3. Pacific J. Math. v.130 Scale-invariant measurability in abstract Wiener space D. M. Chung
4. Supplemento ai Rendiconti del Circolo Mathematico di Palermo. Serie Ⅱ v.8 Stability theorems for the Feynman integral G. W. Johnson;D. L. Skoug
5. J. Math. phys. v.25 no.5 A bounded convergence theorems for the Feynman integral G. W. Johnson
6. the Feynman integral and Feynman's operator caculus. Mem. Amer. Soc. v.62 no.351 Generalized Dyson Seres, Generalized Feynman Diagrams G. W. Johnson;M. L. Lapidus
7. J. of K.M.S. v.29 no.2 The Wiener integral over paths in abstract Wiener space K. S. Ryu
8. The existence theorem of the operator-valued function space integral over paths in abstract Wiener space K. S. Ryu;S. C. Yoo