Hilbert space formalism of quantum mechanics without the Hilbert space axiom

The Hilbert Space Axiom in Quantum Mechanics

A note on the Hilbert space formalism of quantum mechanics

Observables and states in the Hilbert space formalism of quantum mechanics

An improved formulation of some theorems and axioms in the axiomatic foundation of the Hilbert space structure of quantum mechanics

The Phase Space Formalism for Quantum Mechanics and C* Axioms

The quantum mechanical Hilbert space formalism and the quantum mechanical probability space of the outcomes of measurements