Extreme points and linear isometries of the domain of a closed *-derivation in C(K)

Toshiko MATSUMOTO; Seiji WATANABE

doi:10.2969/jmsj/04820229

Extreme points and linear isometries of the domain of a closed ^*-derivation in C(K)

Toshiko MATSUMOTO, Seiji WATANABE

著者情報

ジャーナルフリー

1996 年 48 巻 2 号 p. 229-254

DOI https://doi.org/10.2969/jmsj/04820229

詳細

Published: 1996 Received: 1993/09/24 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : Extreme points and linear isometries of the domain of a closed *-derivation in C(K)
Right : Extreme points and linear isometries of the domain of a closed ^*-derivation in C(K)

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Department of Mathematical Science Graduate School of Science and Technology Niigata University
2) Department of Mathematics Niigata University

訂正後 :
1) Department of Mathematical Science Graduate School of Science and Technology Niigata University
2) Department of Mathematics Faculty of Science Niigata University

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) C. J. K. Batty, Unbounded derivations of commutative C^*-algebras, Comm. Math. Phys., 61 (1978), 261-266.
2) C. J. K. Batty, Derivations on compact spaces, Proc. London Math. Soc. (3), 42 (1981), 299-330.
3) O. Bratteli and D. Robinson, Unbounded derivations of C^*-algebras, Comm. Math. Phys., 42 (1975), 253-268.
4) O. Bratteli and D. Robinson, Unbounded derivations of C*-algebras II, Comm. Math. Phys., 46 (1976), 11-30.
5) O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics I, Springer-Verlag, Heidelberg-Berlin-New York, 1979.
6) M. Cambern, Isometries of certain Banach algebras, Studia Math., 25 (1965), 217-225.
7) M. Cambern and J. T. Pathak, Isometries of spaces of differentiable functions, Math. Japon., 26 (1981), 253-260.
8) N. Dunford and J. T. Schwartz, Linear Operators Part I; General Theory, Interscience, New York, 1958.
9) F. H. Goodman, Closed derivations in commutative C^*-algebras, J. Funct. Anal., 39 (1980), 308-346.
10) K. Jarosz and V. D. Pathak, Isometry between function spaces, Trans. Amer. Math. Sac., 305 (1988), 193-206.
11) H. Kurose, An example of a non quasi-well behaved derivations in C(I), J. Funct. Anal., 43 (1981), 193-201.
12) H. Kurose, Closed derivations in C(I), Tohoku Math. J. (2), 35 (1983), 341-347.
13) K. de Leeuw, Banach spaces of Lipschitz functions, Studia Math., 21 (1961), 55- 66.
14) A. McIntosh, Functions and derivations of C^*-algebras, J. Funct. Anal., 31 (1978), 264-275.
15) W. P. Novinger, Linear isometries of subspaces of continuous functions, Studia Math., 53 (1975), 273-276.
16) T. Okayasu and M. Takagaki, Linear isometries of function spaces, RIMS Kokyûroku, Kyoto Univ., 743, pp. 130-140.
17) S. Ota, Certain operator algebras induced by *-derivations in C^*-algebras on an indefinite inner product space, J. Funct. Anal., 30 (1978), 238-244.
18) S. Ota, Closed derivations in C^*-algebras, Math. Ann., 257 (1981), 239-250.
19) N. V. Rao and A. K. Roy, Linear isometries of some function spaces, Pacific J. Math., 38 (1971), 177-192.
20) A. K. Roy, Extreme points and linear isometries of the Banach space of Lipschitz functions, Canad. J. Math., 20 (1968), 1150-1164.
21) S. Sakai, The theory of unbounded derivations in C^*-algebras, Lecture Notes, Univ. of Copenhagen and Newcastle upon Tyne, 1977.
22) S. Sakai, Operator algebras in dynamical systems: The theory of unbounded derivations in C^*-algebras, Cambridge University Press, Cambridge, 1991.
23) K.W. Tam, Isometries of certain function spaces, Pacific J. Math., 31 (1969), 233-246.
24) J. Tomiyama, The theory of closed derivations in the algebra of continuous functions on the unit interval, Institute of Mathematics National Tsing Hua University, 1983.

Right : [1] C. J. K. Batty, Unbounded derivations of commutative C^*-algebras, Comm. Math. Phys., 61 (1978), 261-266.
[2] C. J. K. Batty, Derivations on compact spaces, Proc. London Math. Soc. (3), 42 (1981), 299-330.
[3] O. Bratteli and D. Robinson, Unbounded derivations of C^*-algebras, Comm. Math. Phys., 42 (1975), 253-268.
[4] O. Bratteli and D. Robinson, Unbounded derivations of C^*-algebras II, Comm. Math. Phys., 46 (1976), 11-30.
[5] O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics I, Springer-Verlag, Heidelberg-Berlin-New York, 1979.
[6] M. Cambern, Isometries of certain Banach algebras, Studia Math., 25 (1965), 217-225.
[7] M. Cambern and J. T. Pathak, Isometries of spaces of differentiable functions, Math. Japon., 26 (1981), 253-260.
[8] N. Dunford and J. T. Schwartz, Linear Operators Part I: General Theory, Interscience, New York, 1958.
[9] F. H. Goodman, Closed derivations in commutative C^*-algebras, J. Funct. Anal., 39 (1980), 308-346.
[10] K. Jarosz and V. D. Pathak, Isometry between function spaces, Trans. Amer. Math. Sac., 305 (1988), 193-206.
[11] H. Kurose, An example of a non quasi-well behaved derivations in C(I), J. Funct. Anal., 43 (1981), 193-201.
[12] H. Kurose, Closed derivations in C(I), Tôhoku Math. J. (2), 35 (1983), 341-347.
[13] K. de Leeuw, Banach spaces of Lipschitz functions, Studia Math., 21 (1961), 55-66.
[14] A. McIntosh, Functions and derivations of C^*-algebras, J. Funct. Anal., 31 (1978), 264-275.
[15] W. P. Novinger, Linear isometries of subspaces of continuous functions, Studia Math., 53 (1975), 273-276.
[16] T. Okayasu and M. Takagaki, Linear isometries of function spaces, RIMS Kôkyûroku, Kyoto Univ., 743, pp. 130-140.
[17] S. Ota, Certain operator algebras induced by ^*-derivations in C^*-algebras on an indefinite inner product space, J. Funct. Anal., 30 (1978), 238-244.
[18] S. Ota, Closed derivations in C^*-algebras, Math. Ann., 257 (1981), 239-250.
[19] N. V. Rao and A. K. Roy, Linear isometries of some function spaces, Pacific J. Math., 38 (1971), 177-192.
[20] A. K. Roy, Extreme points and linear isometries of the Banach space of Lipschitz functions, Canad. J. Math., 20 (1968), 1150-1164.
[21] S. Sakai, The theory of unbounded derivations in C^*-algebras, Lecture Notes, Univ. of Copenhagen and Newcastle upon Tyne, 1977.
[22] S. Sakai, Operator algebras in dynamical systems: The theory of unbounded derivations in C^*-algebras, Cambridge University Press, Cambridge, 1991.
[23] K. W. Tam, Isometries of certain function spaces, Pacific J. Math., 31 (1969), 233-246.
[24] J. Tomiyama, The theory of closed derivations in the algebra of continuous functions on the unit interval, Institute of Mathematics National Tsing Hua University, 1983.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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