OpenLLM-France/wikimedia huggingface dataset:
# Lake Graham (Tennessee)

Lake Graham (also Graham Lake) is a reservoir in Madison County, Tennessee 5 miles (8.0 km) west of the city of Jackson. It is primarily a recreational lake that also provides wetlands habitat to local wildlife and migratory birds. The lake is owned and managed by the Tennessee Wildlife Resources Agency (TWRA). The TWRA Region One offices are located at the lake, and it is the largest lake managed by the Agency. The lake is impounded by a 51 foot (16 m) high earthen dam with an uncontrolled spillway.

## History

The lake was first proposed in 1971, with Madison County Commissioner John Graham leading efforts to obtain the $2.8 million in federal, state, and county funds for the lake's construction. Originally known as Lake Madison, named after the county it is located in, it was informally referred to by commissioners as Lake Graham. In 1981, Governor Lamar Alexander ordered the dam across Brown's Creek closed during a ceremony at the construction site.
In July 1982, the Madison County commission officially recommended the lake be renamed to Lake Graham, which was denied by the Tennessee Wildlife Resources Commission. By September of that year, the Tennessee Wildlife Resources Commission reached an agreement to name it after Graham, who was at that time a member of the commission and was initially against the renaming to avoid appearances of favoritism until they agreed to name the road leading to the lake after Sen. Lowell Thomas, another supporter of the project, and the renaming received the support of a number of state senators and representatives.
The lake was projected to be opened in early 1983. By late 1982, the projects had been revised to on-or-about January 1, 1983, but significant rain in early December 1982 caused a rapid rise in the lake's levels. By December 16, 1982, the water had crested the spillway and the lake was declared filled and open.

## Ecology

The primary purpose of the lake was to provide a habitat for sport fishing near Jackson, though the history of the fish population in the lake has been troubled. In 1981, while the lake was still filling and before fishing was allowed, a group of individuals illegally stocked crappie in the lake. The species then exploded, out-competing other species due to the unbalanced, unnaturally large numbers of fish added to the lake. In 1989, the TWRA began the process of lowering the water levels in the lake to concentrate the prey species to allow for predation by other fish, such as bass and catfish. These efforts were only partly successful, though, and later the TWRA was forced to conduct a large scale fish kill to bring populations under control. By the early 1990s, crappie populations had decreased to unacceptably low levels, and re-stocking programs were started.
# Banfi

Banfi is a surname. It may also refer to:

## People

* Antonio Banfi (1886–1957), Italian philosopher and senator
* Emilio Banfi (1881–unknown), Italian track and field athlete
* Karina Banfi (born 1972), Argentine politician
* Lino Banfi (born 1936), Italian film actor and presenter
* Raúl Banfi (1914 –unknown), Uruguayan football player
* Rosanna Banfi (born 1963), Italian actress

## Places

* Banfi, Croatia, village in northern Croatia
# Cozes

Cozes (French pronunciation:) is a commune in the Charente-Maritime department in southwestern France in the region of Nouvelle-Aquitaine. Its inhabitants are Cozillions . The town of Cozes forms part of the urban community Royan, which, as of 2006, had a total population of 72,136 inhabitants.
It is part of the rural hinterland of Royan and is a hub of commercial activities and crafts.
The small town, is grouped around a church dating back to 12th and 13th centuries. Its perfectly preserved market place attracts increasing numbers of tourists, who are brought into the area by its proximity to the resorts on the Coast of Beauty (La Côte de Beauté). It annually hosts various cultural events including the 'Southern Exposure' festival, dedicated to the cultures of Africa.

## Population

| Year | Pop. | ±% p.a. |
| 1793 | 1,882 | — |
| 1800 | 1,886 | +0.03% |
| 1806 | 1,706 | −1.66% |
| 1821 | 1,796 | +0.34% |
| 1831 | 1,871 | +0.41% |
| 1836 | 1,948 | +0.81% |
| 1841 | 1,906 | −0.43% |
| 1846 | 1,914 | +0.08% |
| 1851 | 1,890 | −0.25% |
| 1856 | 1,889 | −0.01% |
| 1861 | 1,885 | −0.04% |
| 1866 | 1,898 | +0.14% |
| 1872 | 1,828 | −0.62% |
| 1876 | 1,850 | +0.30% |
| 1881 | 1,837 | −0.14% |
| 1886 | 1,758 | −0.88% |
| 1891 | 1,688 | −0.81% |
| 1896 | 1,600 | −1.07% |
| Year | Pop. | ±% p.a. |
| 1901 | 1,553 | −0.59% |
| 1906 | 1,552 | −0.01% |
| 1911 | 1,446 | −1.40% |
| 1921 | 1,379 | −0.47% |
| 1926 | 1,370 | −0.13% |
| 1931 | 1,433 | +0.90% |
| 1936 | 1,441 | +0.11% |
| 1946 | 1,331 | −0.79% |
| 1954 | 1,446 | +1.04% |
| 1962 | 1,579 | +1.11% |
| 1968 | 1,653 | +0.77% |
| 1975 | 1,697 | +0.38% |
| 1982 | 1,746 | +0.41% |
| 1990 | 1,730 | −0.12% |
| 1999 | 1,830 | +0.63% |
| 2007 | 1,925 | +0.63% |
| 2012 | 2,041 | +1.18% |
| 2017 | 2,142 | +0.97% |
Source: EHESS and INSEE (1968-2017) :
# South East Purbeck (ward)

South East Purbeck is an electoral ward in Dorset. Since 2019, the ward has elected 1 councillor to Dorset Council.

## Geography

The South East Purbeck ward is rural and covers the southern and western parts of the Isle of Purbeck outside Swanage. It includes the villages of Acton, Corfe Castle, Kimmeridge and Studland.

## Councillors

| Election | Councillors | Councillors |
| 2019 | | Cherry Brooks (Conservative) |
| 2024 | | Ben Wilson (Liberal Democrats) |

## Election
### 2019 Dorset Council election

2019 Dorset Council election: South East Purbeck (1 seat) :
| Party | Party | Candidate | Votes | % | ±% |
| | Conservative | Cherry Louise Brooks | 499 | 30.7 | |
| | Independent | Nigel Dragon | 451 | 27.7 | |
| | Liberal Democrats | Mandy Platts | 284 | 17.5 | |
| | Labour | George Holden | 191 | 11.7 | |
| | UKIP | John Barnes | 117 | 7.2 | |
| | Independent | Matt Etherington | 84 | 5.2 | |
| Majority | Majority | Majority | | | |
| Turnout | Turnout | Turnout | | 46.80 | |
| | Conservative win (new seat) | Conservative win (new seat) | Conservative win (new seat) | Conservative win (new seat) | Conservative win (new seat) |

### 2024 Dorset Council election

South East Purbeck :
| Party | Party | Candidate | Votes | % | ±% |
| | Liberal Democrats | Ben Wilson | 848 | 57.8 | +40.3 |
| | Conservative | Cherry Louise Brooks* | 523 | 35.7 | +5.0 |
| | Labour | Peter Copp | 95 | 6.5 | −5.2 |
| Turnout | Turnout | Turnout | 1,466 | 42.57 | |
| | Liberal Democrats gain from Conservative | Liberal Democrats gain from Conservative | Swing | | |
# SPSU

SPSU may refer to:
* Southern Polytechnic State University
* Sir Padampat Singhania University
# 1993 Brown Bears football team

The 1993 Brown Bears football team was an American football team that represented Brown University during the 1993 NCAA Division I-AA football season. Brown tied for fourth in the Ivy League.
In their fourth and final season under head coach Mickey Kwiatkowski, the Bears compiled a 4–6 record and were outscored 267 to 190. Todd Hunter and Walton Smith were the team captains.
The Bears' 3–4 conference record tied for fourth place in the Ivy League standings. They were outscored 183 to 127 by Ivy opponents.
Brown played its home games at Brown Stadium in Providence, Rhode Island.

## Schedule

| Date | Opponent | Site | Result | Attendance |
| September 18 | at Yale | Yale BowlNew Haven, CT | W 12–3 | 7,967 |
| September 25 | at Lehigh* | Goodman StadiumBethlehem, PA | L 35–42 | 9,264 |
| October 2 | Rhode Island* | Brown StadiumProvidence, RI (rivalry) | L 7–30 | 4,429 |
| October 9 | Princeton | Brown StadiumProvidence, RI | L 16–34 | 3,571 |
| October 16 | Bucknell* | Brown StadiumProvidence, RI | W 21–12 | 3,653 |
| October 23 | at No. 25 Penn | Franklin FieldPhiladelphia, PA | L 9–34 | 19,121 |
| October 30 | Cornell | Brown StadiumProvidence, RI | L 3–21 | 2,174 |
| November 6 | Harvard | Brown StadiumProvidence, RI | W 43–29 | 6,129 |
| November 13 | at Dartmouth | Memorial FieldHanover, NH | L 16–39 | 5,913 |
| November 20 | Columbia | Brown StadiumProvidence, RI | W 28–23 | 2,420 |
| *Non-conference gameRankings from The Sports Network Poll released prior to the game ||||||
# Glenea baramensis

Glenea baramensis is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1950. It is known from Borneo.
# Herman Koehler (end)

Herman Jules Koehler (July 15, 1873 – September–December 1931) was an American college football player, amateur ice hockey player and outdoorsman.

## Biography

Koehler was born in Upper Montclair, New Jersey on July 15, 1873.
Koehler was an experienced outdoorsman and made several trips across Labrador and northern Quebec. He is believed to have died sometime between September and December in 1931 while trying to pass Labrador from Kuujjuaq with fellow New Jerseyman Fred Connell and guide Jimmy Martin from Cartwright. Koehler's and Connell's bodies were found five kilometers apart while Martin's body was never found.

### University of North Carolina

He was a prominent end for the North Carolina Tar Heels football team of the University of North Carolina. He was selected second-team for an all-time Carolina football team in 1934. Dr. Joel Whitaker put him on his all-time team, ranking him the second best end in the history of the school up to that time. He notes that Koehler came to the University with experience, for he played on the Orange Athletic Club with Frank Coyne.
Koehler was selected All-Southern in 1898 and 1899.

### Ice hockey

Koehler was also an amateur ice hockey player with his hometown team Montclair Athletic Club in Montclair, New Jersey. He captained the team during the 1896–97 season, and also appeared with the team in the American Amateur Hockey League in 1897–98 and 1898–99.
# Southern Africa Direct

Southern Africa Direct (or SA Direct as it is known) is a lifestyle and culture television channel, broadcast in the United Kingdom. The channel streams programmes online through its website. The channel was also available on the Sky Digital platform until January 2010.
The channel markets itself as the first 'Destination TV' channel in the UK and is primarily focused on Southern Africa. The channel offers programmes about lifestyle, culture, travel, tourism, commerce, and trade.
SA Direct was initially broadcast on the Sky Digital platform. It was removed from the Sky EPG on 9 October 2009, however, the channel returned to Sky on 6 November 2009. It started off only broadcasting two hours a day (noon – 2 pm), and increased its hours to cover the afternoon and evening. The channel was acting as a placeholder until the EPG slot was sold to another broadcaster. On 11 January 2010, Takbeer TV began testing after purchasing the Southern Africa Direct EPG slot and replaced it on 14 January. Despite the fact that SA Direct is not currently being broadcast on any major television platform, the channel is still operating as a commercial business over the internet. The channel's website claims that SA Direct will return to television broadcasts in the future.
# Kado

Kado may refer to:
* Kadu people
* Ikebana, also known as Kadō, Japanese flower arrangement
* Kado, Kalewa, Burma
* Kado, Togo
* KADO-CD, a low-power television station (channel 36, virtual 40) licensed to serve Shreveport, Louisiana, United States
* Kado or Ka-do, an island in North Korea
* Kado: The Right Answer, anime
# South Dakota's 2nd congressional district

South Dakota's 2nd congressional district is an obsolete district. It was created after the 1910 census and was eliminated as a result of the redistricting cycle after the 1980 census. Members were elected at-large until the formation of individual districts after the 1910 census. From 1913 until 1933, it covered much of northeastern South Dakota, including the cities of Aberdeen, Brookings, Huron, and Watertown. When South Dakota's 3rd congressional district was eliminated after the 1930 census, the 2nd district was relocated to cover all of the counties in South Dakota west of the Missouri River. Population changes eventually moved its boundaries further east. During the 97th Congress, it covered all but the 21 easternmost counties in the state.

## List of representatives

| Member (Residence) | Party | Years | Cong ress | Electoral history |
| District established March 4, 1913 |||||
| Charles H. Burke (Pierre) | Republican | March 4, 1913 – March 3, 1915 | 63rd | Redistricted from the at-large district and re-elected in 1912 Retired to run for U.S. senator. |
| Royal C. Johnson (Aberdeen) | Republican | March 4, 1915 – March 3, 1933 | 64th 65th 66th 67th 68th 69th 70th 71st 72nd | Elected in 1914. Re-elected in 1916. Re-elected in 1918. Re-elected in 1920. Re-elected in 1922. Re-elected in 1924. Re-elected in 1926. Re-elected in 1928. Re-elected in 1930. Lost re-election. |
| Theodore B. Werner (Rapid City) | Democratic | March 4, 1933 – January 3, 1937 | 73rd 74th | Elected in 1932. Re-elected in 1934 Lost re-election. |
| Francis H. Case (Custer) | Republican | January 3, 1937 – January 3, 1951 | 75th 76th 77th 78th 79th 80th 81st | Elected in 1936. Re-elected in 1938. Re-elected in 1940. Re-elected in 1942. Re-elected in 1944. Re-elected in 1946. Re-elected in 1948. Retired to run for U.S. senator. |
| E. Y. Berry (McLaughlin) | Republican | January 3, 1951 – January 3, 1971 | 82nd 83rd 84th 85th 86th 87th 88th 89th 90th 91st | Elected in 1950. Re-elected in 1952. Re-elected in 1954. Re-elected in 1956. Re-elected in 1958. Re-elected in 1960. Re-elected in 1962. Re-elected in 1964. Re-elected in 1966. Re-elected in 1968. Retired. |
| James Abourezk (Rapid City) | Democratic | January 3, 1971 – January 3, 1973 | 92nd | Elected in 1970. Retired to run for U.S. senator. |
| James Abdnor (Kennebec) | Republican | January 3, 1973 – January 3, 1981 | 93rd 94th 95th 96th | Elected in 1972. Re-elected in 1974. Re-elected in 1976. Re-elected in 1978. Retired to run for U.S. senator. |
| Clint Roberts (Presho) | Republican | January 3, 1981 – January 3, 1983 | 97th | Elected in 1980. Redistricted to the at-large district and lost re-election. |
| District dissolved January 3, 1983 |||||
# Kallakottai

Kallakkottai is a village in the Gandaravakottai revenue block of Pudukkottai district, Tamil Nadu, India.

## Demographics

As per the 2001 census, Kallakottai had a total population of 3894 with 1976 males and 2008 females. Out of the total population 1968 people were literate.
# Kadal (1968 film)

Kadal is a 1968 Indian Malayalam-language film, directed by M. Krishnan Nair and produced by P. Subramaniam. The film stars Madhu, Sharada, Thikkurissy Sukumaran Nair and Shobha. The film had musical score by M. B. Sreenivasan.

## Cast

* Madhu as Antony
* Sharada as Mary
* K. P. Ummer as Lazar
* Rajasree as Rajeena
* S. P. Pillai as Peter
* Bahadoor as Paul
* K. V. Shanthi as Reetha
* Nellikode Bhaskaran as Lopez
* Baby Shobha
* Baby Sree Thikkurissi
* Baby Vijaya

## Soundtrack

The music was composed by M. B. Sreenivasan and the lyrics were written by Sreekumaran Thampi.
| No. | Song | Singers | Lyrics |
| 1 | "Aarum Kaanaathayyayya" | M. S. Padma, Renuka | Sreekumaran Thampi |
| 2 | "Chirikkumpol Koode" | S. Janaki | Sreekumaran Thampi |
| 3 | "Kadalinenthu Moham" | K. J. Yesudas | Sreekumaran Thampi |
| 4 | "Kallanmaar Kaaryakkaaraayi" | K. J. Yesudas, Kamukara | Sreekumaran Thampi |
| 5 | "Manushyan Kothikkunnu" | Kamukara | Sreekumaran Thampi |
| 6 | "Paadaanaavaatha Raagam" | L. R. Eeswari | Sreekumaran Thampi] |
| 7 | "Valayum Vanchiyum" | K. J. Yesudas, [Kamukara], Gomathy | Sreekumaran Thampi |
# Kalinino, Azerbaijan

40°29′N 46°22′E﻿ / ﻿40.483°N 46.367°E﻿ / 40.483; 46.367
Kalinino is a village in the Goygol Rayon of Azerbaijan. It is named after Mikhail Kalinin, a Soviet revolutionary and a member of the Politburo of the Communist Party of the Soviet Union.
# Kagerō no Tsuji: Inemuri Iwane Edo Zōshi

Kagerō no Tsuji: Inemuri Iwane Edo Zōshi (陽炎の辻〜居眠り磐音 江戸双紙〜) is a (2007-2010) Japanese television series, first shown on NHK on July 19, 2007, based on the Inemuri Iwane novels by Yasuhide Saeki.

## Cast

* Koji Yamamoto as Sakazaki Iwane
* Noriko Nakagoshi as Okon
* Ikkei Watanabe as Imazuya Kichiemon
* Masaomi Kondō as Yoshizō
* Rei Dan as Oen
* Hiromi Kitagawa as Osaki
* Yuko Fueki as Kobayashi Nao
* Shun Shioya as Kobayashi Kinpei
* Sei Hiraizumi as Sakazaki Masayoshi
* Masao Komatsu as Kinbei
* Natsuki Harada as Okine
* Riki Takeuchi as Sakai Taizō
# Southern State Correctional Facility (New Jersey)

Southern State Correctional Facility (SSCF) was a prison for men located in Delmont, Maurice River Township, New Jersey, United States. It was a part of the New Jersey Department of Corrections. It was adjacent to Bayside State Prison.
Its operations began in 1983. Its buildings consisted of prefabricated units. Prisoners lived in dormitory housing as opposed to individual cells. It closed in 2022.
# Southern Star Concrete

Southern Star Concrete, Inc. or simply Southern Star is a concrete supply business headquartered in Irving, Texas. Southern Star is owned by Cementos Argos S.A., the largest cement producer in Colombia, South America. Cementos Argos is subsidiary of Inversiones Argos, which in turn belongs to a larger conglomerate called Grupo Empresarial Antioqueño based in Medellín, Colombia.
Argos acquired full ownership of Southern Star Concrete in November 2005 in a purchase agreement with the former owners, Texas Growth Fund and Austin Ventures, both based in Austin, Texas.
In 2019, Southern Star sold their Arkansas assets to SRM Concrete, a privately-owned materials supply company based out of Nashville, Tennessee.
Then in 2021, Argos sold the Dallas/Fort Worth portion of Southern Star to SRM Concrete.
Argos currently only operates the Houston area Southern Star locations.
# Spain at the 1994 Winter Olympics

Spain competed at the 1994 Winter Olympics in Lillehammer, Norway.

## Competitors

The following is the list of number of competitors in the Games.
| Sport | Men | Women | Total |
| Alpine skiing | 4 | 3 | 7 |
| Cross-country skiing | 3 | 0 | 3 |
| Figure skating | 0 | 1 | 1 |
| Freestyle skiing | 1 | 1 | 2 |
| Total | 8 | 5 | 13 |

## Alpine skiing
### Men

| Athlete | Event | Race 1 | Race 2 | Total | Total |
| Athlete | Event | Time | Time | Time | Rank |
| Vicente Tomas | Super-G | | | 1:38.02 | 39 |
| Xavier Ubeira | Super-G | | | 1:37.60 | 38 |
| Luis Cristobal | Super-G | | | 1:37.31 | 36 |
| Luis Cristobal | Giant Slalom | 1:33.34 | DNF | DNF | – |
| Xavier Ubeira | Giant Slalom | 1:32.07 | 1:27.28 | 2:59.35 | 28 |
| Xavier Ubeira | Slalom | DNF | – | DNF | – |
| Ovidio García | Slalom | DNF | – | DNF | – |
| Vicente Tomas | Slalom | 1:06.71 | 1:06.73 | 2:13.44 | 20 |
Men's combined
| Athlete | Downhill | Slalom | Slalom | Total | Total |
| Athlete | Time | Time 1 | Time 2 | Total time | Rank |
| Ovidio García | 1:46.48 | DSQ | – | DSQ | – |
| Vicente Tomas | 1:44.32 | 55.68 | 51.61 | 3:31.61 | 28 |
| Xavier Ubeira | 1:42.78 | 53.17 | 50.97 | 3:26.92 | 25 |

### Women

| Athlete | Event | Race 1 | Race 2 | Total | Total |
| Athlete | Event | Time | Time | Time | Rank |
| María José Rienda | Super-G | | | 1:24.65 | 29 |
| Ainhoa Ibarra | Super-G | | | 1:24.50 | 27 |
| Mónica Bosch | Giant Slalom | 1:25.62 | 1:15.61 | 2:41.23 | 22 |
| María José Rienda | Giant Slalom | 1:24.62 | 1:14.83 | 2:39.45 | 21 |
| Ainhoa Ibarra | Giant Slalom | 1:23.36 | 1:13.31 | 2:36.67 | 17 |
| María José Rienda | Slalom | DNF | – | DNF | – |
| Ainhoa Ibarra | Slalom | DNF | – | DNF | – |
| Mónica Bosch | Slalom | 1:03.79 | 1:02.32 | 2:06.11 | 23 |

## Cross-country skiing
### Men

| Event | Athlete | Race | Race |
| Event | Athlete | Time | Rank |
| 10 km C | Jordi Ribó | 27:21.2 | 57 |
| 10 km C | Juan Jesús Gutiérrez | 27:06.0 | 47 |
| 10 km C | Carlos Vicente | 27:01.4 | 44 |
| 15 km pursuit$^1$ F | Jordi Ribó | 42:47.6 | 47 |
| 15 km pursuit$^1$ F | Carlos Vicente | 41:13.3 | 32 |
| 15 km pursuit$^1$ F | Juan Jesús Gutiérrez | 41:00.0 | 28 |
| 30 km F | Juan Jesús Gutiérrez | 1'19:47.3 | 30 |
| 30 km F | Jordi Ribó | 1'19:33.8 | 29 |
| 50 km C | Carlos Vicente | 2'21:03.5 | 42 |
| 50 km C | Jordi Ribó | 2'19:21.9 | 34 |
| 50 km C | Juan Jesús Gutiérrez | 2'14:22.5 | 19 |
$^1$ Starting delay based on 10 km results.
C = Classical style, F = Freestyle

## Figure skating
### Women

| Athlete | SP | FS | TFP | Rank |
| Marta Andrade | 21 | 21 | 31.5 | 20 |

## Freestyle skiing
### Men

| Athlete | Event | Qualification | Qualification | Qualification | Final | Final | Final |
| Athlete | Event | Time | Points | Rank | Time | Points | Rank |
| José Rojas | Moguls | 26.36 | 22.49 | 24 | did not advance | did not advance | did not advance |

### Women

| Athlete | Event | Qualification | Qualification | Qualification | Final | Final | Final |
| Athlete | Event | Time | Points | Rank | Time | Points | Rank |
| Patricia Portillo | Moguls | 53.58 | 9.15 | 24 | did not advance | did not advance | did not advance |
# Kallir

Kallir is a surname. Notable people with this surname include:
* Eleazar ben Kalir (c. 570–c. 640), Byzantine Jew and a Hebrew poet
* Eleazar ben Eleazar Kallir (1728–1805), Hungarian rabbi
* Jane Kallir, American art dealer, curator and author
* Lilian Kallir, Czech-born American pianist
* Otto Kallir, Austrian American art historian, author, publisher
# Kadison transitivity theorem

In mathematics, Kadison transitivity theorem is a result in the theory of C*-algebras that, in effect, asserts the equivalence of the notions of topological irreducibility and algebraic irreducibility of representations of C*-algebras. It implies that, for irreducible representations of C*-algebras, the only non-zero linear invariant subspace is the whole space.
The theorem, proved by Richard Kadison, was surprising as a priori there is no reason to believe that all topologically irreducible representations are also algebraically irreducible.

## Statement

A family ${\mathcal {F}}$ of bounded operators on a Hilbert space ${\mathcal {H}}$ is said to act topologically irreducibly when $\{0\}$ and ${\mathcal {H}}$ are the only closed stable subspaces under ${\mathcal {F}}$. The family ${\mathcal {F}}$ is said to act algebraically irreducibly if $\{0\}$ and ${\mathcal {H}}$ are the only linear manifolds in ${\mathcal {H}}$ stable under ${\mathcal {F}}$.
Theorem. If the C*-algebra ${\mathfrak {A}}$ acts topologically irreducibly on the Hilbert space ${\mathcal {H}},\{y_{1},\cdots ,y_{n}\}$ is a set of vectors and $\{x_{1},\cdots ,x_{n}\}$ is a linearly independent set of vectors in ${\mathcal {H}}$, there is an $A$ in ${\mathfrak {A}}$ such that $Ax_{j}=y_{j}$. If $Bx_{j}=y_{j}$ for some self-adjoint operator $B$, then $A$ can be chosen to be self-adjoint.
Corollary. If the C*-algebra ${\mathfrak {A}}$ acts topologically irreducibly on the Hilbert space ${\mathcal {H}}$, then it acts algebraically irreducibly.
# Speak the speech

"Speak the speech" is a famous speech from Shakespeare's Hamlet (1601). In it, Hamlet offers directions and advice to a group of actors whom he has enlisted to play for the court of Denmark.
The speech itself has played two important roles independent of the play. It has been analyzed as a historical document for clues about the nature of early modern acting practices and it has also been used as a contemporary guide to the performance of Shakespearean drama.
While there is some justification for each of these approaches, they should be distinguished from other, far less valid assertions: on the one hand, that Hamlet expresses the opinions of Shakespeare on the art of acting in a straightforward and unproblematic way; on the other, that the speech offers a proto-Stanislavskian view of the art of acting. The first elides the difference between author and character, while the second ignores the historical specificity of the discourses and meanings attached to theatrical performance.