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Rigged Hilbert Space and the Dirac Calculus

Lectures on Quantum Mechanics, 2020

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Quasi *-Algebras of Operators in Rigged Hilbert Spaces

2002
In this chapter, we will study families of operators acting on a rigged Hilbert space, with a particular interest in their partial algebraic structure. In Section 10.1 the notion of rigged Hilbert space D[t] ↪ H ↪ D × [t ×] is introduced and some examples are presented. In Section 10.2, we consider the space.L(D, D ×) of all continuous linear maps from
Atsushi Inoue, Camillo Trapani, Jean-Pierre Antoine +2 more
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Representations on Rigged Spaces and Hilbert $$C^*$$-Modules

2020
This chapter provides an introduction to $*$-representations of a $*$-algebra A on rigged spaces and Hilbert $C^*$-modules. A right (or left) rigged space is a right (or left) A-module equipped with an A-valued sesquilinear mapping which is compatible with the module action.
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Dirac Kets, Gamow Vectors and Gel'fand triplets : the rigged Hilbert space formulation of quantum mechanics : lectures in mathematical physics at the University of Texas at Austin

, 1989
A. Bohm, J. Dollard, M. Gadella
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Resonances in the Rigged Hilbert Space and Lax-Phillips Scattering Theory

, 2003
Y. Strauss
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Non-negative Self-adjoint Extensions in Rigged Hilbert Space

, 2014
Y. Arlinskii̇̆, S. Belyi
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Physical representations of Gamow states in a rigged Hilbert space