C∗-algebras (pronounced "C-star") are an important area of research in functional analysis, a branch of mathematics. A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed under the operation of taking adjoints of operators. C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables. This line of research began with Werner Heisenberg's matrix mechanics and in a more mathematically developed...

Phi (uppercase Φ, lowercase or ; Ancient Greek: ϕεῖ, pheî, [pʰé͜e]; modern Greek: φι, fi, [fi]; English: /faɪ/) is the 21st letter of the Greek alphabet. In Ancient Greek, it represented an aspirated voiceless bilabial plosive ([pʰ]), which was the origin of its usual romanization as "ph". In modern Greek, it represents a voiceless labiodental fricative ([f]) and is correspondingly romanized as "f". Its origin is uncertain but it may be that phi originated as the letter qoppa and initially represented the sound /kʷʰ/ before shifting to Classical Greek [pʰ]. In traditional Greek numerals, phi has...