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Jorda, i.e., spaces in which all sets M of continuous seminorms of cardinality up to g have an upper bound in P(E). On the other hand, we study bilinear maps b from a product of locally convex spaces E_1 and E_2 to a locally convex space F, which admit \"product estimates\" in the sense that for all p_{i,j} in P(F), i,j=1,2,..., there exist"},"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":"1112.1824","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-12-08T13:04:19Z","cross_cats_sorted":[],"title_canon_sha256":"cdc3197fc6440cd948ebed402720cb5dbf6611aba2ed59804a1c6f8796495304","abstract_canon_sha256":"47b72eda13cef6ff3f148e2eab886bc8d929ed6e2d19cffae9bce669d4dc39df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:24.668976Z","signature_b64":"VYAXLQayehexdenFZ9IWdD/v5kEonwA33ueaA+YrC3+vZd8VbYXkWSI+sFCpy07VJKRLZf8J/KD+G9Upqv9iAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4099bc77fd9898c4517117eac2aa30f87d3ab92c7fdd95c31c291911a92742b","last_reissued_at":"2026-05-18T03:55:24.668491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:24.668491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Upper bounds for continuous seminorms and special properties of bilinear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Helge Glockner","submitted_at":"2011-12-08T13:04:19Z","abstract_excerpt":"If E is a locally convex topological vector space, let P(E) be the pre-ordered set of all continuous seminorms on E. 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