The notions of compact convex variation and compact convex subdifferential for the mappings from a segment into a locally convex space (LCS) are studied. In the case of an arbitrary complete LCS, each indefinite Bochner integral has compact variation and each strongly absolutely continuous and compact subdifferentiable a.e. mapping is an indefinite Bochner integral. 0. Introduction and prelimin...

In order to characterise the C∗ -algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in C, we compute its principal symbol. We show then that the Szegö projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral. Mathematics Subject Classification (2000). Primary 32A25; Secondary 47L15, 47G30.

We describe a unified approach to Herglotz, Bochner and BochnerMinlos theorems using a combination of Daniell integral and nonstandard analysis. The proofs suggest a natural extension of the last two theorems to the case when the characteristic function is not continuous. This extension is proven and is demonstrated to be the best one possible. The goal of this paper is to show how the classic ...

X iv :m at h/ 04 06 10 8v 1 [ m at h. FA ] 6 J un 2 00 4 QUADRATIC REVERSES OF THE CONTINUOUS TRIANGLE INEQUALITY FOR BOCHNER INTEGRAL OF VECTOR-VALUED FUNCTIONS IN HILBERT SPACES SEVER S. DRAGOMIR Abstract. Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are prov...

In this paper, we study the minimax estimation of the Bochner integral μk(P ) := ∫

Some reverses of the continuous triangle inequality for Bochner integral of vectorvalued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

In this paper, we prove the existence of continuous solutions of a Volterra integral inclusion involving the Henstock-Kurzweil-Pettis integral. Since this kind of integral is more general than the Bochner, Pettis and Henstock integrals, our result extends many of the results previously obtained in the single-valued setting or in the set-valued case.

We characterize the class of finite measure spaces (T ,T , μ) which guarantee that for a correspondenceφ from (T ,T , μ) to a general Banach space the Bochner integral of φ is convex. In addition, it is shown that if φ has weakly compact values and is integrably bounded, then, for this class of measure spaces, the Bochner integral of φ is weakly compact, too. Analogous results are provided with...