PreprintCC BY 4.0arXiv
Pettis integrability of functions with values in separable symmetrically-normed ideals and related norm estimates
Abstract
In this paper we will investigate Pettis integrability of 𝒞∘Φ(ℋ)-valued functions. We will study weakly* integrable ℬ(ℋ)-valued functions and establish sufficient conditions for such functions to be Pettis integrable as 𝒞∘Φ(ℋ)-valued functions. In addition, we prove the inequality |∫E𝒜*ℬdμ|Φ(p) leqslant |𝒜|Lqs·|√[p]∫E|ℬ|pdμ|Φ(p), where Φ(p) is p-modification of the function Φ and the functions 𝒜 and ℬ belong to the suitable spaces of operator-valued functions. Finally, under some additional integrability assumptions on ℬ we provide similar estimates of the Pettis norm.
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BibTeX
@misc{krstic2026pettis,
title = {{Pettis integrability of functions with values in separable symmetrically-normed ideals and related norm estimates}},
author = {Mihailo Krstić and Matija Milović and Stefan Milošević},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.02790},
eprint = {2607.02790},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.02790},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pettis integrability of functions with values in separable symmetrically-normed ideals and related norm estimates
AU - Mihailo Krstić
AU - Matija Milović
AU - Stefan Milošević
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2607.02790
UR - https://arxiv.org/abs/2607.02790
AB - In this paper we will investigate Pettis integrability of 𝒞^∘_Φ(ℋ)-valued functions. We will study weakly^* integrable ℬ(ℋ)-valued functions and establish sufficient conditions for such functions to be Pettis integrable as 𝒞^∘_Φ(ℋ)-valued functions. In addition, we prove the inequality |∫_E𝒜^*ℬdμ|_Φ^(p) leqslant |𝒜|_L^q_s·|√[p]∫_E|ℬ|^pdμ|_Φ^(p), where Φ^(p) is p-modification of the function Φ and the functions 𝒜 and ℬ belong to the suitable spaces of operator-valued functions. Finally, under some additional integrability assumptions on ℬ we provide similar estimates of the Pettis norm.
ER -