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Let $f$ be a continuous function on the Euclidean closure of $\\mathbb{B}^n$. It is well-known that then the corresponding Toeplitz operator $T_f$ is Fredholm if and only if $f$ has no zeros on the boundary $\\partial\\mathbb{B}^n$. As a consequence, the essential spectrum of $T_f$ is given by the boundary values of $f$. We extend this result to all operators in"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.04553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-05-12T13:08:30Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"33668f877a31e853a667187dac9cf1cbcecf9e7462569786e0f079a7ec4e7507","abstract_canon_sha256":"863c4fb283aa0ba6c65fcdd0a614cf576990744625273b5d8b8b69262cfa4520"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:46.515665Z","signature_b64":"QQIzzVJFM0czQUTKapzEpELoyxnuaJExjCtPDWpZmbI+e/OJKC3B4Suj17DwPjKlEOrWgn53dMnYoLuJ7WxRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af6d946a8f002e06d03a1599c92336db65b8aa133612cbacc34fbd029f4c3da9","last_reissued_at":"2026-05-18T00:18:46.515117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:46.515117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Essential Spectrum of Toeplitz Operators on the Unit Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Raffael Hagger","submitted_at":"2017-05-12T13:08:30Z","abstract_excerpt":"In this paper we study the Fredholm properties of Toeplitz operators acting on weighted Bergman spaces $A^p_{\\nu}(\\mathbb{B}^n)$, where $p \\in (1,\\infty)$ and $\\mathbb{B}^n \\subset \\mathbb{C}^n$ denotes the $n$-dimensional open unit ball. Let $f$ be a continuous function on the Euclidean closure of $\\mathbb{B}^n$. It is well-known that then the corresponding Toeplitz operator $T_f$ is Fredholm if and only if $f$ has no zeros on the boundary $\\partial\\mathbb{B}^n$. As a consequence, the essential spectrum of $T_f$ is given by the boundary values of $f$. 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