Gemara

Rami bar Chama: Semichah (pressing on the neck of a Korban) must be with all one's strength.

Question - Beraisa: "Daber El Benei Yisrael...v'Somach" - Benei Yisrael do Semichah; Benos Yisrael do not;

R. Yosi and R. Shimon say, Semichah is Reshus (optional) for Benos Yisrael.

R. Yosi: Aba Elazar told me that once they brought a Shelamim to the Ezras Nashim for women to do Semichah on it. This is not because Semichah applies to women. Rather, it was to please them.

If Semichah must be with all one's strength, how can we allow using a Korban (to support oneself on it) just to please women?!

Answer: The women were told to do Semichah softly (without all their strength).

Rosh Hashanah 33a - Mishnah: We do not stop children from blowing a Shofar (on Rosh Hashanah).

Inference: We stop women from blowing.

Contradiction (Beraisa): We do not stop women from blowing.

Resolution (Abaye): The Mishnah is like R. Yehudah (who forbids women to do Semichah), and the Beraisa is like R. Yosi and R. Shimon (who permit).

Eruvin 96a - Beraisa: Michal bas Sha'ul used to wear Tefilin. The wife of Yonah (the Navi) was Olah l'Regel. Chachamim did not protest against either of them.

Inference: They did not protest against Michal because they held that Tefilin is Mitzvas Aseh she'Lo ha'Zman Gerama (it applies at all times)!

Rejection: Perhaps the Tana (holds that it is Zman Gerama, but he) holds like R. Yosi, who says that Semichah is optional for women (even though they are exempt. For the same reason, Chachamim did not protest against Michal!)

Rishonim

Rambam (Hilchos Tzitzis 3:9): A woman is exempt from Tzitzis. If she wants to wear Tzitzis without a Berachah, she may. Similarly, if she performs any Mitzvah from which she is exempt without a Berachah, we do not protest.

Ra'avad: Some permit her to bless. They bring a proof from Rav Yosef (Bava Kama 87). At first, he would have been happy to hear that the Halachah follows R. Yehudah. If one who is not commanded may not bless, he would be pained to learn that he is exempt!

Kesef Mishneh: This is no proof. Rav Yosef thought that one who is exempt and fulfills without a Berachah is greater than one who is commanded and fulfills with a Berachah.

Migdal Oz: The Ra'avad's proof is that Rav Yosef would be pained to learn that the Berachos he made until now were l'Vatalah. This is not a proof. If he is exempt from all Mitzvos, also Berachah l'Vatalah is not forbidden to him! Also, perhaps Rav Yosef was not saying Berachos on Mitzvos until now, due to his Safek.

Rosh (Rosh Hashanah 4:7): R. Tam says that even though our Stam Tana is like R. Yehudah, the Halachah follows R. Yosi, for Nimuko Imo (he has great reasons to support himself). Also, Michal bas Sha'ul wore Tefilin and Yonah's wife was Oleh l'Regel. Since actions were done, we follow them. Also, a Shelamim was brought to the Ezras Nashim for women to do Semichah on it to please them.

Rashba (Rosh Hashanah 33a DH R. Yosi): Our Mishnah is not a Stam Mishnah teaching that only children may blow, but not women. Rather, it permits children for all agree about them; it does not discuss women, for Tana'im argue about this. However, this is wrong. The Gemara learns from our Mishnah that R. Meir holds that Semichah is not Reshus for women! Nevertheless, the conclusion of all Rishonim is that women may bless, and we do not protest.

Rosh (Kidushin 1:49): R. Tam says that a woman may bless on a Mitzvas Aseh sheha'Zman Gerama, even though she is exempt even mid'Rabanan. Even though the Berachah is unnecessary, mid'Oraisa this is not Shem Shomayim l'Vatalah. A Drashah says that it is (Berachos 33a), but that is only an Asmachta. We find that one who is unsure whether or not he read Shma reads again; we are not concerned for Shem Shomayim l'Vatalah (Berachos 21a).

Note: The Ran (Rosh Hashanah 9b DH ul'Inyan) proves this from the Heter to say 'Emes v'Yatziv' when in doubt. Surely the Rosh also refers to this, for Kri'as Shma itself has no Berachah.

Rosh (ibid.): If one who is not commanded may not bless, Rav Yosef would have been pained to learn that he is exempt! R. Yehudah says that Chachamim objected to Michal for wearing Tefilin. Presumably, this is because she blessed. This shows that R. Yosi permits blessing. However, it is unreasonable for one who is not commanded to bless 'v'Tzivanu'. We cannot prove this from Rav Yosef, for in any case a blind person is Chayav in Mitzvos mid'Rabanan. This is why he was able to Motzi others in Hagadah. R. Yitzchak bar Yehudah proves that women may bless from the Heter for women to read the Torah. R. Tam rejects the proof, for even if the Olah already blessed for his Mitzvah of Talmud Torah, he blesses again for Kri'as ha'Torah (i.e. the Berachah is to honor the Kri'ah). Also, perhaps the Heter for a woman to read was when only the first and last Olim used to bless, and she would be Olah in the middle (and not bless).

Ran (ibid., DH umi'Kol): R. Chanina taught that one who is commanded and fulfills is greater than one who is not commanded and fulfills. This implies that one who is not commanded also gets reward; it is considered that he did a Mitzvah. Since men are commanded and women receive reward, it is proper for them to bless 'v'Tzivanu'.

R. Mano'ach (Hilchos Shofar 2:2): Women may perform the Mitzvos of Shofar, Sukah or Lulav without a Berachah. If a man blows for women, he and they do not bless. Tosfos permits them to bless. This is unreasonable. The Halachah follows our Stam Mishnah (which forbids them to blow) against the argument in the Beraisa. And even if the Halachah follows R. Yosi and R. Shimon, they only allow women to blow. I.e., even on Shabbos we do not decree. We do not allow a Berachah l'Vatalah, which is an Isur mid'Oraisa. It is Sheker for them to say 'Asher Kidshanu...'

Tosfos (Eruvin 96b DH Dilma): One may bless on a Mitzvah that he does, even if he is exempt. However, we cannot prove this from Rav Yosef, for in any case a blind person is Chayav in Mitzvos mid'Rabanan, so he will not be like a Nochri.

Hagahos Maimoniyos (9): Tosfos (Sukah 11A DH d'Rav) says that the Halachah follows R. Shimon, since the Gemara (Zevachim 18b) takes pains to establish all the Tana'im like R. Shimon. Also, the Gemara in Shabbos (25b) establishes the decree of a Sadin like R. Shimon.

Question (Griz Al Rambam Hilchos Berachos 11:16, DH v'Hinei): Why do woman bless Birkas ha'Torah? The Rambam says that women do not bless on Mitzvos from which they are exempt!

Answer (Griz): The Berachah on Torah is not for the Mitzvah. Rather, it is for the Torah itself.

Note: This applies to 'Asher Bochar Banu...', but surely 'Asher Kidshanu b'Mitzvosav v'Tzivanu La'asok...' is for the Mitzvah (Teshuvas Afarkasta d'Anya 2 OC 8 DH v'Od)! Perhaps since they are obligated in one Berachah, they say both. I did not find that the Rambam says that women bless Birkas ha'Torah. The Beis Yosef (OC 47 DH v'Chosav Od) cites the Agur to say that women bless Birkas ha'Torah. Perhaps since we do not disqualify women from Kri'as ha'Torah b'Tzibur due to the Berachah, the Griz assumes that all agree that they may bless.

Poskim

Shulchan Aruch (17:2): A woman is exempt from Tzitzis because it is Mitzvas Aseh sheha'Zman Gerama.

Rema: If she wants to cover herself (with a Talis) and bless, she may, just like any Mitzvas Aseh sheha'Zman Gerama.

Beis Yosef (DH Aval): It is not clear whether or not the Rosh allows women to bless. The Remazim (the Tur's Kitzur Piskei ha'Rosh) in Rosh Hashanah (4:7) say that women may bless, but in Kidushin (1:49) they say that BaHaG's proofs for this were rejected. L'Halachah, we follow the Rambam who forbids, for Safek Berachos Lehakel.

Gra (DH u'Levarech): The Rambam forbids women to bless, for even regarding Mitzvos mid'Rabanan the Gemara asked why we may say 'v'Tzivanu' (Shabbos 23a).

Rema: However, this looks like haughtiness, therefore she should not wear Tzitzis, since it is not an obligation on the person. I.e. one need not buy a garment (with four corners) to become obligated.

Mishnah Berurah (5): The Rema teaches why women do fulfill and bless on a Lulav. Tzitzis is different, for it is not obligatory even on men.

Kaf ha'Chayim (4): At first, the Birkei Yosef (654:2) and Chida objected to women who blessed. When they learned that R. Yakov asked from Shomayim about this and was told that they may bless, they also permitted. Even though the Mechaber says not to, had he heard the answer from Shomayim he would have ruled like it. Regarding this we do not say that 'the Torah is not in Shomayim'. We do not say Safek Berachos Lehakel against a tradition.