{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/305688"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/305688","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"The Cotype of Operators from C(K)","abstract":"In 1987, Jameson [J1] studied the relationship between the (2, 1)-summing norm and the 2-summing norm for operators from l N ∞. He showed that, in general, these norms are not equivalent. At the end of his paper, he observed that the Rademacher cotype 2 constant of operators from l N ∞ lay between these two summing norms, and he asked whether it was indeed equivalent to one of them. Answering this question proved to be very hard. By delicate averaging arguments, I managed to prove that the Rademacher cotype 2 constant for an operator from l N ∞ is very close to its (2, 1)-summing norm; they are within about log log N of each other, and hence, in general, the cotype 2 constant and the 2-summing norms are inequivalent. The techniques used also enabled me to compare the Rademacher and Gaussian cotype p constants for many operators from l N ∞, deducing that these are not the same. Studying this problem also led me to consider quite a different subject. I defined new spaces which are a common generalization of the Lorentz Lp,q and the Orlicz LΦ spaces. As well as rederiving results of Bennett and Rudnick, I sought to calculate the Boyd indices of these new spaces.","abstract_html":"In 1987, Jameson [J1] studied the relationship between the (2, 1)-summing norm and the 2-summing norm for operators from l N ∞. He showed that, in general, these norms are not equivalent. At the end of his paper, he observed that the Rademacher cotype 2 constant of operators from l N ∞ lay between these two summing norms, and he asked whether it was indeed equivalent to one of them. Answering this question proved to be very hard. By delicate averaging arguments, I managed to prove that the Rademacher cotype 2 constant for an operator from l N ∞ is very close to its (2, 1)-summing norm; they are within about log log N of each other, and hence, in general, the cotype 2 constant and the 2-summing norms are inequivalent. The techniques used also enabled me to compare the Rademacher and Gaussian cotype p constants for many operators from l N ∞, deducing that these are not the same. Studying this problem also led me to consider quite a different subject. I defined new spaces which are a common generalization of the Lorentz Lp,q and the Orlicz LΦ spaces. As well as rederiving results of Bennett and Rudnick, I sought to calculate the Boyd indices of these new spaces.","abstract_has_math":false,"creators":["Montgomery-Smith, Stephen"],"institution":"University of Cambridge","degree_name":"PhD","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1988,"date_issued":"1988","date_published":"1988","updated_at":"2026-07-22T22:24:01Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/cf5e121d-f205-4aad-a89f-339701f88b2d/download","https://www.rioxx.net/licenses/all-rights-reserved/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.52766","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Montgomery-Smith, Stephen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["1988"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/305688"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/cf5e121d-f205-4aad-a89f-339701f88b2d/download","https://www.rioxx.net/licenses/all-rights-reserved/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.52766"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/7b89f900-577b-4053-ba3f-ff5c13fd684f/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In 1987, Jameson [J1] studied the relationship between the (2, 1)-summing norm and the 2-summing norm for operators from l N ∞. He showed that, in general, these norms are not equivalent. At the end of his paper, he observed that the Rademacher cotype 2 constant of operators from l N ∞ lay between these two summing norms, and he asked whether it was indeed equivalent to one of them. Answering this question proved to be very hard. By delicate averaging arguments, I managed to prove that the Rademacher cotype 2 constant for an operator from l N ∞ is very close to its (2, 1)-summing norm; they are within about log log N of each other, and hence, in general, the cotype 2 constant and the 2-summing norms are inequivalent. The techniques used also enabled me to compare the Rademacher and Gaussian cotype p constants for many operators from l N ∞, deducing that these are not the same. Studying this problem also led me to consider quite a different subject. I defined new spaces which are a common generalization of the Lorentz Lp,q and the Orlicz LΦ spaces. As well as rederiving results of Bennett and Rudnick, I sought to calculate the Boyd indices of these new spaces."]},{"key":"dc:format.checksum.md5","label":"Dc Format Checksum Md5","values":["107ff1c3d407122081498a2dda3ead66","87eda9de84448d1f82354d60eee3eb5f"]},{"key":"dc:title","label":"Title","values":["The Cotype of Operators from C(K)"]}]}],"canonical_facts":{"dc:creator":["Montgomery-Smith, Stephen"],"dc:date.issued":["1988"],"dc:description.abstract":["In 1987, Jameson [J1] studied the relationship between the (2, 1)-summing norm and the 2-summing norm for operators from l N ∞. He showed that, in general, these norms are not equivalent. At the end of his paper, he observed that the Rademacher cotype 2 constant of operators from l N ∞ lay between these two summing norms, and he asked whether it was indeed equivalent to one of them. Answering this question proved to be very hard. 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