On ε-phase-isometries between the positive cones of continuous function spaces
Let K and T be compact Hausdorff spaces, C+(K)={f∈C(K):f(k)≥0forallk∈K} be the positive cone of C(K). In this paper, we prove that if K is a compact Hausdorff perfectly normal space, then for every ε-phase-isometry F:C+(K)→C+(T), there are nonempty closed subset S⊂T and an additive isometry V:C+(K)→...
Saved in:
| Published in: | Indian journal of pure and applied mathematics Vol. 56; no. 2; pp. 728 - 736 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Heidelberg
Springer Nature B.V
01.06.2025
|
| Subjects: | |
| ISSN: | 0019-5588, 0975-7465 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Let K and T be compact Hausdorff spaces, C+(K)={f∈C(K):f(k)≥0forallk∈K} be the positive cone of C(K). In this paper, we prove that if K is a compact Hausdorff perfectly normal space, then for every ε-phase-isometry F:C+(K)→C+(T), there are nonempty closed subset S⊂T and an additive isometry V:C+(K)→C+(S) defined as V(f)=limn→∞F(2nf)|S2n for each f∈C+(K) satisfying that ‖F(f)|S-V(f)‖≤32ε,forallf∈C+(K).Moreover, if F is almost surjective, then there exists a unique homeomorphism γ:T→K such that |F(f)(t)-f(γ(t))|≤32ε,t∈T,f∈C+(K). |
|---|---|
| AbstractList | Let K and T be compact Hausdorff spaces, C+(K)={f∈C(K):f(k)≥0forallk∈K} be the positive cone of C(K). In this paper, we prove that if K is a compact Hausdorff perfectly normal space, then for every ε-phase-isometry F:C+(K)→C+(T), there are nonempty closed subset S⊂T and an additive isometry V:C+(K)→C+(S) defined as V(f)=limn→∞F(2nf)|S2n for each f∈C+(K) satisfying that ‖F(f)|S-V(f)‖≤32ε,forallf∈C+(K).Moreover, if F is almost surjective, then there exists a unique homeomorphism γ:T→K such that |F(f)(t)-f(γ(t))|≤32ε,t∈T,f∈C+(K). |
| Author | An, Aimin Wang, Wenting |
| Author_xml | – sequence: 1 givenname: Wenting surname: Wang fullname: Wang, Wenting – sequence: 2 givenname: Aimin surname: An fullname: An, Aimin |
| BookMark | eNotj81KAzEUhYNUsK2-gKuA6-hNMpkkSyn-QaEbXZdkvKFTNBl7M4oP5mv4TI7o6nycxfk4CzbLJSNj5xIuJYC9IqmVagUoLQCMbMTnEZuDt0bYpjWziUF6YYxzJ2xBtAdoNXg_Z5tN5t9fYtgFQtFTecV66JF4xPqBmHndIR8K9bV_R95NUuIl_ULt81hG4mnMXe1L5jSEDumUHafwQnj2n0v2dHvzuLoX683dw-p6LQbpdBWqwWh9k1qvfNAxBmdU8jFMByTGLlmZvLEBXUxNcs2zkp2zClIrp1pB0Et28bc7HMrbiFS3-zIe8qTcamWMVM7oVv8AGUtUkg |
| ContentType | Journal Article |
| Copyright | The Indian National Science Academy 2023. |
| Copyright_xml | – notice: The Indian National Science Academy 2023. |
| DOI | 10.1007/s13226-023-00514-y |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 0975-7465 |
| EndPage | 736 |
| GroupedDBID | -~X 06D 0R~ 0VY 199 1N0 203 2JN 2KG 2LR 30V 4.4 406 408 40D 5GY 67Z 8UJ 95. 96X AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAPKM AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYZH AAZMS ABAKF ABDBE ABDZT ABECU ABFSG ABFTV ABHLI ABJNI ABJOX ABKCH ABMQK ABQBU ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABXPI ACAOD ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACPIV ACSTC ACZOJ ADHHG ADHIR ADKNI ADKPE ADTPH ADURQ ADYFF ADZKW AEFQL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETCA AEVLU AEXYK AEZWR AFBBN AFDZB AFHIU AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJRNO ALMA_UNASSIGNED_HOLDINGS AMKLP AMXSW AMYLF AMYQR ANMIH AOCGG ARMRJ ASPBG ATHPR AVWKF AXYYD AYJHY AZFZN BAPOH BGNMA CSCUP DDRTE DNIVK DPUIP DU5 EBLON EBS EIOEI ESBYG FERAY FIGPU FNLPD FRRFC GGCAI GGRSB GJIRD GNWQR GQ7 HF~ HMJXF HRMNR IKXTQ IWAJR IXD J-C J0Z JBSCW JZLTJ KOV LLZTM M4Y M~E N9A NPVJJ NQJWS NU0 O93 O9J OK1 P2P P9R PT4 R9I ROL RSV S1Z S27 S3B SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W48 WK8 Z45 ZMTXR ~A9 |
| ID | FETCH-LOGICAL-p183t-24eb794f6929a3bba852f9ba0231ebcf71f957ae8bf4f84d21c8720f6195720a3 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001109999800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0019-5588 |
| IngestDate | Mon Sep 29 04:23:03 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-p183t-24eb794f6929a3bba852f9ba0231ebcf71f957ae8bf4f84d21c8720f6195720a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 3255128536 |
| PQPubID | 2044203 |
| PageCount | 9 |
| ParticipantIDs | proquest_journals_3255128536 |
| PublicationCentury | 2000 |
| PublicationDate | 20250601 |
| PublicationDateYYYYMMDD | 2025-06-01 |
| PublicationDate_xml | – month: 06 year: 2025 text: 20250601 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Heidelberg |
| PublicationPlace_xml | – name: Heidelberg |
| PublicationTitle | Indian journal of pure and applied mathematics |
| PublicationYear | 2025 |
| Publisher | Springer Nature B.V |
| Publisher_xml | – name: Springer Nature B.V |
| SSID | ssj0063099 |
| Score | 2.3604143 |
| Snippet | Let K and T be compact Hausdorff spaces, C+(K)={f∈C(K):f(k)≥0forallk∈K} be the positive cone of C(K). In this paper, we prove that if K is a compact Hausdorff... |
| SourceID | proquest |
| SourceType | Aggregation Database |
| StartPage | 728 |
| SubjectTerms | Banach spaces Function space Mathematical functions Mathematicians |
| Title | On ε-phase-isometries between the positive cones of continuous function spaces |
| URI | https://www.proquest.com/docview/3255128536 |
| Volume | 56 |
| WOSCitedRecordID | wos001109999800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 0975-7465 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0063099 issn: 0019-5588 databaseCode: M~E dateStart: 19700101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 0975-7465 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0063099 issn: 0019-5588 databaseCode: RSV dateStart: 20100201 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3NbhMxELZC6QEOFVBQoaXygXIzynrj9fpYqlQcQoJo2uYWrb22CGq3S5NG7QvwRrwGz8T4bzclEoIDl83KidbazKf58zczCL3hpRQq4xkxkqfEHsQRSaUivCxLpsHgJo7yfzbgw2E-mYhPnc73WAuzvOBVld_eivq_ihrWQNi2dPYfxN08FBbgHoQOVxA7XP9K8CMQ51H_4D0j9RcwUWQ2v7p0Y7PmDSnLlUc5ttbSkdV941nLWp9VN5YTa62dAwboGxVYhl8j5901M1jpOFHHM4gieLSXTSvYxmE_D2npc-0mU7TJB6eb7GSx1fQDZS1N6l760XKr7W5NeYxXt4kgjPm5fe90yDtyRnjPD4iIKtj3Fg9Qoyv6lIfKcW-afZXCutbvhipoUE6WUZ0S19Wd3LU2Lp7rD0fT49PBYDruT8Zv62_ETh-zp_RhFMsD9JByJiw18PPJWbToWdoVPowKrxOKr3wJ5u-brhl156mMn6CtEGLgQw-Np6ijq2fo8cdWKNtoNKrwzx9rAMEBIBh-iiNAsAMIvjK4BQiOAMEeIM_R6XF_fPSBhNEapAYdviC0pyVoYpOBd1ykUhY5o0bIwnYD1FIZnhjBeKFzaXom75U0UTmnXQPhNoPPIn2BNirYfQfhJDclzbRMqQvOk1xpWaikEGWpuJT6JdqL_8c0YHM-TSGSBc-IpdmrP3-9ix61qNtDG4vrG_0abarlYja_3ndi-gXQ1WXM |
| linkProvider | Springer Nature |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+%CE%B5-phase-isometries+between+the+positive+cones+of+continuous+function+spaces&rft.jtitle=Indian+journal+of+pure+and+applied+mathematics&rft.au=Wang%2C+Wenting&rft.au=An%2C+Aimin&rft.date=2025-06-01&rft.pub=Springer+Nature+B.V&rft.issn=0019-5588&rft.eissn=0975-7465&rft.volume=56&rft.issue=2&rft.spage=728&rft.epage=736&rft_id=info:doi/10.1007%2Fs13226-023-00514-y&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0019-5588&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0019-5588&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0019-5588&client=summon |