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Cowen states that, for a symbol $\\varphi \\in L^{\\infty }, \\; \\varphi \\equiv \\bar{f}+g \\;\\;(f,g\\in H^{2})$, the Toeplitz operator $T_{\\varphi }$ acting on the Hardy space of the unit circle is hyponormal if and only if $f=c+T_{\\bar{h}}g,$ for some $c\\in {\\mathbb C}$, $h\\in H^{\\infty }$, $\\left\\| h\\right\\| _{\\infty}\\leq 1.$ \\ In this note we consider possible versions of this result in the {\\it Bergman} space case. \\ Concretely, we consider Toeplitz operators on the Bergman space of the unit disk, with symbols of the form $$\\varphi \\equiv \\alpha z^n+\\beta z^m +\\gamma \\o"},"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":"1610.09596","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-10-30T02:47:41Z","cross_cats_sorted":[],"title_canon_sha256":"0cd851695c1d8796e25e14cf3e650efbf30296600e2b073ab42517206225b3bf","abstract_canon_sha256":"1f3affd117400069c6a2ecebba0d779deea5deefbadab6912a629ed39092274e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:37.183240Z","signature_b64":"eI3lmqP5r3nL9I9YVdI9vIqPoqzISJjZvJMrRRnEpTGOPIpymrGaAAF2EeoZMhdn5yWb0IlTB2NM9Hg6c4YcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6091ebdabffd2024090c9d46bce0431e6d0429e13a088b0ef4ec362e90e34744","last_reissued_at":"2026-05-18T00:57:37.182695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:37.182695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Necessary Condition for the Hyponormality of Toeplitz Operators on the Bergman Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Raul E. 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