“Peter Orno”的意思、由来-开放百科全书

Beginning in 1974, the fictitious Peter Orno (alternatively, Peter Ørno, P. Ørno, and P. Orno) appeared as the author of research papers in mathematics. According to Robert Phelps,^[1] the name "P. Orno" is a pseudonym that was inspired by "porno", an abbreviation for "pornography".^[2]^[2] Orno's short papers have been called "elegant" contributions to functional analysis. Orno's theorem on linear operators is important in the theory of Banach spaces. Research mathematicians have written acknowledgments that have thanked Orno for stimulating discussions and for Orno's generosity in allowing others to publish his results. The Mathematical Association of America's journals have also published more than a dozen problems whose solutions were submitted in the name of Orno.

Biography

Peter Orno appears as the author of short papers written by an anonymous mathematician; thus "Peter Orno" is a pseudonym. According to Robert R. Phelps,^[1] the name "P. Orno" was inspired by "porno", a shortening of "pornography".^[2]^[2]

Orno's papers list his affiliation as the Department of Mathematics at Ohio State University. This affiliation is confirmed in the description of Orno as a "special creation" at Ohio State in Pietsch's History of Banach spaces and linear operators.^[4]

The publications list of Ohio State mathematician Gerald Edgar includes two items that were published under the name of Orno. Edgar indicates that he published them "as Peter Ørno".^[5]

Research

His papers feature "surprisingly simple" proofs and solutions to open problems in functional analysis and approximation theory, according to reviewers from Mathematical Reviews: In one case, Orno's "elegant" approach was contrasted with the previously known "elementary, but masochistic" approach. Peter Orno's "permanent interest and sharp criticism stimulated" the "work" on Lectures on Banach spaces of analytic functions by Aleksander Pełczyński, which includes several of Orno's unpublished results.^[6] Tomczak-Jaegermann thanked Peter Orno for his stimulating discussions.^[7]

Selected publications

Peter Orno has published in research journals and in collections; his papers have always been short, having lengths between one and three pages. Orno has also established himself as a formidable solver of mathematical problems in peer-reviewed journals published by the Mathematical Association of America.

Research papers

According to Mathematical Reviews ({{MR|374859}}), this paper proves the following theorem, which has come to be known as "Orno's theorem": Suppose that E and F are Banach lattices, where F is an infinite-dimensional vector space that contains no Riesz subspace that is uniformly isomorphic to the sequence space equipped with the supremum norm. If each linear operator in the uniform closure of the finite-rank operators from E to F has a Riesz decomposition as the difference of two positive operators, then E can be renormed so that it is an L-space (in the sense of Kakutani and Birkhoff).^[8]^[9]^[10]^[11]^[12]^[13]^[14]

According to Mathematical Reviews ({{MR|458156}}), Orno proved the following theorem: The series ∑f_k unconditionally converges in the Lebesgue space of absolutely integrable functions L₁[0,1] if and only if, for each k and every t, we have f_k(t)=a_kg(t)w_k(t), for some sequence (a_k)∈l₂, some function g∈L₂[0,1], and for some orthonormal sequence (w_k) in L₂[0,2] {{MR|458156}}. Another result is what Joseph Diestel described as the "elegant proof" by Orno of a theorem of Bennet, Maurey and Nahoum.^[15]

In this paper, Orno solves an eight-year-old problem posed by Ivan Singer, according to Mathematical Reviews ({{MR|454485}}).

Still circulating as an "underground classic", {{as of|2018|October|lc=yes}} this paper had been cited sixteen times.^[16] In it, Orno solved a problem posed by Jonathan M. Borwein. Orno characterized sequentially reflexive Banach spaces in terms of their lacking bad subspaces: Orno's theorem states that a Banach space X is sequentially reflexive if and only if the space of absolutely summable sequences ℓ1 is not isomorphic to a subspace of X.

Problem-solving

Between 1976 and 1982, Peter Orno contributed problems or solutions that appeared in eighteen issues of Mathematics Magazine, which is published by the Mathematical Association of America (MAA).^[17]

In 2006, Orno solved a problem in the American Mathematical Monthly, another peer-reviewed journal of the MAA:

Context

Peter Orno is one of several pseudonymous contributors in the field of mathematics. Other pseudonymous mathematicians active in the 20th century include Nicolas Bourbaki, John Rainwater, M. G. Stanley, and H. C. Enos.^[18]

See also

Besides connoting "pornography", the name "Ørno" features a non-standard symbol:

Notes

1. ^¹{{harvtxt|Phelps|2002}}
2. ^¹In the index to his Sequences and series in Banach spaces, Joseph Diestel places Peter Orno under the letter "p" as "P. ORNO", with all-capital letters in Diestel's original. {{harv|Diestel|1984|p=259}}.
3. ^The Garden of Constants is located at Ohio State University, according to {{harv|Ross Mathematics Program|2012|loc=Caption "Garden of Constants at Ohio State"}}:

{{cite web|url=http://www.math.osu.edu/ross/|accessdate=12 April 2012|title=Ross Mathematics Program June 18 –July 27, 2012|publisher=Ohio State University|last=Ross Mathematics Program|authorlink=Ross Mathematics Program|ref=harv|year=2012}}
4. ^{{harvtxt|Pietsch|2007|p=602}}
5. ^Gerald A. Edgar, Publications, Ohio State University. Retrieved March 18, 2012; archived by WebCite at https://www.webcitation.org/66GaKYk03. Items that Edgar claims as his work, but identifies as having been attributed to "Peter Ørno", are the problem proposed in Mathematics Magazine 52 (1979), 179, and the problem solution presented in American Mathematical Monthly 113 (2006) 572–573.
6. ^{{harvtxt|Pełczyński|1977|p=2}}
7. ^{{harvtxt|Tomczak-Jaegermann|1979|p=273}}
8. ^{{Cite book |last1=Abramovich |first1=Y. A. |last2=Aliprantis |first2=C. D. |authorlink2=C. D. Aliprantis |chapter=Positive Operators |editor1-last=Johnson |editor1-first=W. B. |editor1-link=William B. Johnson (mathematician) |editor2-last=Lindenstrauss |editor2-first=J. |editor2-link=Joram Lindenstrauss |year=2001 |title=Handbook of the Geometry of Banach Spaces |publisher=Elsevier Science B. V. |volume=1 |pages=85–122 |isbn=978-0-444-82842-2 |doi=10.1016/S1874-5849(01)80004-8 |series=Handbook of the Geometry of Banach Spaces |ref=harv}}
9. ^{{cite journal |last=Yanovskii |first=L. P. |year=1979 |title=Summing and serially summing operators and characterization of AL-spaces |journal=Siberian Mathematical Journal |volume=20 |issue=2 |pages=287–292 |doi=10.1007/BF00970037 |ref=harv}}
10. ^{{cite journal |last=Wickstead |first=A. W. |year=2010 |title=When are all bounded operators between classical Banach lattices regular? |url=http://www.qub.ac.uk/puremaths/Preprints/5_2010.pdf |ref=harv}}
11. ^{{cite book |last=Meyer-Nieberg |first=P. |year=1991 |title=Banach Lattices |series=Universitext |publisher=Springer-Verlag |isbn=3-540-54201-9 |mr=1128093}}
12. ^In {{MR|763464}}, Manfred Wulff noted that Orno's theorem implies several propositions in the following paper:{{cite journal |last=Xiong |first=H. Y. |year=1984 |title=On whether or not L(E,F) = L_r(E,F) for some classical Banach lattices E and F |journal=Nederl. Akad. Wetensch. Indag. Math. |volume=46 |issue=3 |pages=267–282 |ref=harv}}
13. ^In {{MR|763464}}, Manfred Wolff noted that Orno's theorem has a good exposition and proof in the following textbook:{{cite book |last=Schwarz |first=H.-U. |year=1984 |title=Banach Lattices and Operators |series=Teubner-Texte zur Mathematik [Teubner Texts in Mathematics] |volume=71 |page=208 |publisher=BSB B. G. Teubner Verlagsgesellschaft |mr=781131}}
14. ^{{cite book |last=Abramovich |first=Y. A. |year=1990 |chapter=When each continuous operator is regular |editor-last=Leifman |editor-first=L. J. |title=Functional Analysis, Optimization, and Mathematical economics |pages=133–140 |publisher=Clarendon Press |isbn=0-19-505729-5 |mr=1082571}}
15. ^{{harvtxt|Diestel|1984|p=[https://books.google.com/books?ei=_r6mTeTKCtXP4wack-WWCg&id=UVmqAAAAIAAJ&sig=ACfU3U1kEOrQn0AR8EhBkhhiz38G4hjSbw&focus=searchwithinvolume&q=orno 190]}}
16. ^{{cite web |title=On J. Borwein's concept of sequentially reflexive Banach spaces |via=Google Scholar |url=https://scholar.google.com/scholar?q=On%20J.%20Borwein's%20concept%20of%20sequentially%20reflexive%20Banach%20spaces%20%C3%98rno%201991 |access-date=Oct 9, 2018}}
17. ^"Problems" sections of Mathematics Magazine in which Peter Orno is one of the contributing authors are: [https://www.jstor.org/stable/2690199 Vol. 49, No. 3 (May 1976), pp. 149–154]; [https://www.jstor.org/stable/2690127 Vol. 49, No. 4 (September 1976), pp. 211–218]; [https://www.jstor.org/stable/2689756 Vol. 50, No. 1 (January 1977), pp. 46–53]; [https://www.jstor.org/stable/2690222 Vol. 50, No. 4 (September 1977), pp. 211–216]; [https://www.jstor.org/stable/2690154 Vol. 51, No. 2 (March 1978), pp. 127–132]; [https://www.jstor.org/stable/2690005 Vol. 51, No. 3 (May 1978), pp. 193–201]; [https://www.jstor.org/stable/2689475 Vol. 51, No. 4 (September 1978), pp. 245–249]; [https://www.jstor.org/stable/2689977 Vol. 52, No. 1 (January 1979), pp. 46–55]; [https://www.jstor.org/stable/2689851 Vol. 52, No. 2 (March 1979), pp. 113–118]; [https://www.jstor.org/stable/2690284 Vol. 52, No. 3 (May 1979), pp. 179–184]; [https://www.jstor.org/stable/2690032 Vol. 53, No. 1 (January 1980), pp. 49–54]; [https://www.jstor.org/stable/2689961 Vol. 53, No. 2 (March 1980), pp. 112–117]; [https://www.jstor.org/stable/2690110 Vol. 53, No. 3 (May 1980), pp. 180–186]; [https://www.jstor.org/stable/2689622 Vol. 53, No. 4 (September 1980), pp. 244–251]; [https://www.jstor.org/stable/2690443 Vol. 54, No. 2 (March 1981), pp. 84–87]; [https://www.jstor.org/stable/2689635 Vol. 54, No. 4 (September 1981), pp. 211–214]; [https://www.jstor.org/stable/2689990 Vol. 54, No. 5 (November 1981), pp. 270–274]; and [https://www.jstor.org/stable/2690087 Vol. 55, No. 3 (May 1982), pp. 177–183].
18. ^¹²Another pseudonymous mathematician, John Rainwater, "is not as old or famous as N. Bourbaki (who may still be alive) but he is clearly older than Peter Orno .... (At least one of his authors had an interest in pornography, hence P. Orno.) He is also older than M. G. Stanley (with four papers) and H. C. Enoses [sic.] (with only two)." {{harv|Phelps|2002}}