{"cited_by_count":868353,"description":"This cluster of papers covers a wide range of topics in the theory of Banach spaces and operators, including functional analysis, topological vector spaces, holomorphic functions, summing operators, Bohr inequality, Lipschitz functions, geometric aspects, and approximation theory.","display_name":"Advanced Banach Space Theory","domain_id":"3","external_ids":{"openalex":"https://openalex.org/T11545","wikipedia":"https://en.wikipedia.org/wiki/Banach_space"},"field_id":"26","id":"T11545","keywords":[{"display_name":"Banach spaces","id":"banach-spaces","score":0.4392,"url":"https://openalex.org/keywords/banach-spaces"},{"display_name":"bounded linear operators","id":"bounded-linear-operators","score":0.4143,"url":"https://openalex.org/keywords/bounded-linear-operators"},{"display_name":"Lp spaces","id":"lp-spaces","score":0.3302,"url":"https://openalex.org/keywords/lp-spaces"},{"display_name":"Banach-Steinhaus theorem","id":"banach-steinhaus-theorem","score":0.5641,"url":"https://openalex.org/keywords/banach-steinhaus-theorem"},{"display_name":"normed spaces","id":"normed-spaces","score":0.5587,"url":"https://openalex.org/keywords/normed-spaces"},{"display_name":"function spaces","id":"function-spaces","score":0.2703,"url":"https://openalex.org/keywords/function-spaces"},{"display_name":"Banach space geometry","id":"geometry-of-banach-spaces","score":0.8625,"url":"https://openalex.org/keywords/geometry-of-banach-spaces"},{"display_name":"locally convex spaces","id":"locally-convex-spaces","score":0.6636,"url":"https://openalex.org/keywords/locally-convex-spaces"},{"display_name":"Banach lattices","id":"banach-lattices","score":0.8228,"url":"https://openalex.org/keywords/banach-lattices"},{"display_name":"dual spaces","id":"dual-spaces","score":0.5175,"url":"https://openalex.org/keywords/dual-spaces"},{"display_name":"compact operators","id":"compact-operators","score":0.3641,"url":"https://openalex.org/keywords/compact-operators"},{"display_name":"Banach algebras","id":"banach-algebras","score":0.2401,"url":"https://openalex.org/keywords/banach-algebras"},{"display_name":"topological vector spaces","id":"topological-vector-spaces","score":0.5805,"url":"https://openalex.org/keywords/topological-vector-spaces"},{"display_name":"vector lattices","id":"vector-lattices","score":0.7397,"url":"https://openalex.org/keywords/vector-lattices"},{"display_name":"Orlicz spaces","id":"orlicz-spaces","score":0.3937,"url":"https://openalex.org/keywords/orlicz-spaces"},{"display_name":"operator ideals","id":"operator-ideals","score":0.7523,"url":"https://openalex.org/keywords/operator-ideals"},{"display_name":"spaces of continuous functions","id":"spaces-of-continuous-functions","score":0.5543,"url":"https://openalex.org/keywords/spaces-of-continuous-functions"},{"display_name":"Hahn-Banach theorem","id":"hahn-banach-theorem","score":0.7585,"url":"https://openalex.org/keywords/hahn-banach-theorem"},{"display_name":"Baire category theorem","id":"baire-category-theorem","score":0.4295,"url":"https://openalex.org/keywords/baire-category-theorem"},{"display_name":"separable Banach spaces","id":"separable-banach-spaces","score":0.622,"url":"https://openalex.org/keywords/separable-banach-spaces"},{"display_name":"vector measures","id":"vector-measures","score":0.7425,"url":"https://openalex.org/keywords/vector-measures"},{"display_name":"sequence spaces","id":"sequence-spaces","score":0.2442,"url":"https://openalex.org/keywords/sequence-spaces"},{"display_name":"unconditional bases","id":"unconditional-bases","score":0.7217,"url":"https://openalex.org/keywords/unconditional-bases"},{"display_name":"extreme points","id":"extreme-points","score":0.2023,"url":"https://openalex.org/keywords/extreme-points"},{"display_name":"inner product spaces","id":"inner-product-spaces","score":0.33,"url":"https://openalex.org/keywords/inner-product-spaces"}],"legacy_keywords":["Banach Spaces","Operators","Functional Analysis","Topological Vector Spaces","Holomorphic Functions","Summing Operators","Bohr Inequality","Lipschitz Functions","Geometric Aspects","Approximation Theory"],"openalex_id":"https://openalex.org/T11545","source_created_date":"2024-01-23T15:27:11","source_updated_date":"2026-10-17T03:02:00","subfield_id":"2610","url":"/topics/T11545","works_api_url":"https://api.openalex.org/works?filter=topics.id:T11545","works_count":91921,"label":"Advanced Banach Space Theory","provider":"openalex","revision":"5ef68401c0970117","taxonomy_revision":"f050b5d4780b1289","title":"Advanced Banach Space Theory","kind":"topic-directory","aeo_cohort":"topic-directory","catalogue_revision":"f050b5d4780b1289","numeric_address":"36249008587317369","address_version":"morton4x16-v1","coordinates":[3,26,2610,11545],"answer_status":"Directory metadata; local answer requires separate source review","truth_status":"Subject descriptor, not a factual answer or a demonstrated knowledge gap","reviewed_answer":null}