{"paper":{"title":"Regular biorthogonal pairs and Psuedo-bosonic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hiroshi Inoue, Mayumi Takakura","submitted_at":"2016-05-20T10:03:26Z","abstract_excerpt":"The first purpose of this paper is to show a method of constructing a regular biorthogonal pair based on the commutation rule: $ab-ba=I$ for a pair of operators $a$ and $b$ acting on a Hilbert space ${\\cal H}$ with inner product $( \\cdot | \\cdot )$. Here, sequences $\\{ \\phi_{n} \\}$ and $\\{ \\psi_{n} \\}$ in a Hilbert space ${\\cal H}$ are biorthogonal if $( \\phi_{n} | \\psi_{m})= \\delta_{nm}$, $n,m=0,1, \\cdots$, and they are regular if both $D_{\\phi} \\equiv Span \\{ \\phi_{n} \\}$ and $D_{\\psi} \\equiv Span \\{ \\psi_{n} \\}$ are dense in ${\\cal H}$. Indeed, the assumption to construct the regular biorth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06269","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}