# Some new characterizations of intrinsic transversality in Hilbert spaces

## TL;DR

This paper provides new dual and primal space characterizations of intrinsic transversality in Hilbert spaces, unifying existing conditions and addressing open research questions in the field.

## Contribution

It introduces novel primal space characterizations of intrinsic transversality, complementing dual space results and clarifying the property in Hilbert spaces.

## Key findings

- New dual space characterizations of intrinsic transversality.
- Primal space characterizations of the property.
- Unified understanding of transversality variants.

## Abstract

Motivated by a number of research questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports several new characterizations of the intrinsic transversality property in Hilbert spaces. Our dual space results clarify the picture of intrinsic transversality, its variants and the only existing sufficient dual condition for subtransversality, and actually unify them. New primal space characterizations of the intrinsic transversality which is originally a dual space condition lead to new understanding of the property in terms of primal space elements for the first time. As a consequence, the obtained analysis allows us to address a number of research questions asked by the two aforementioned researchers about the intrinsic transversality property in the Hilbert space setting.